Category: Mathematics

  • [Solved] it is a MATHEMATICS QUESTION

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    [>Trigonometry homework help](https://www.sweetstudy.com/fields/mathematics-trigonometry) Three resistors of **2 Ω, 3 Ω and 6 Ω** are connected in **parallel**. This combination is connected in **series** with a **4 Ω** resistor. The whole circuit is connected to a **12 V battery**. Find: 1. Total r…

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    [>Trigonometry homework help](https://www.sweetstudy.com/fields/mathematics-trigonometry)

    Three resistors of **2 Ω, 3 Ω and 6 Ω** are connected in **parallel**.

    This combination is connected in **series** with a **4 Ω** resistor.

    The whole circuit is connected to a **12 V battery**.

    Find:

    1. Total resistance of the circuit

    2. Total current from the battery

    3. Current flowing through each of the 2 Ω, 3 Ω and 6 Ω resistors

    4. Potential difference across the parallel combination

  • [Solved] i need five charts done asap

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    [>Statistics homework help](https://www.sweetstudy.com/fields/mathematics-statistics) histogram line chart pie chart bar chart box and whisker

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    [>Statistics homework help](https://www.sweetstudy.com/fields/mathematics-statistics)

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  • [Solved] home work

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    [>Statistics homework help](https://www.sweetstudy.com/fields/mathematics-statistics) **files (1)** – ## DLV4.docx **## DLV4.docx** **Competency** Evaluate hypothesis tests for population parameters from one population. **Project Deliverable tie to Competency** In the fourth assignment, you will nee…

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    [>Statistics homework help](https://www.sweetstudy.com/fields/mathematics-statistics)

    **files (1)**

    – ## DLV4.docx

    **## DLV4.docx**

    **Competency**

    Evaluate hypothesis tests for population parameters from one population.

    **Project Deliverable tie to Competency**

    In the fourth assignment, you will need to make data-driven decisions by evaluating claims about a single population. You will be tasked with completing several hypothesis tests, which follow a structured process: stating hypotheses, selecting the appropriate test, calculating test statistics, and making conclusions based on evidence. These tasks directly align with the competency for evaluating hypothesis tests for population parameters from one population. You will also be demonstrating your knowledge of identifying potential errors, such as Type I and Type II Errors.

    **Scenario**

    After analyzing the data, you have determined a few hypotheses that you would like to test. In the Excel Workbook provided below, use the data to run two hypothesis tests and determine a conclusion based on the evidence provided. Proceed to explain your process to your boss.

    **Instructions**

    The Excel Workbook contains five tabs. The first tab contains the instructions. The second tab, labeled "data", contains the raw data that will be used for your calculations. The next three tabs contain questions for you to answer. Ensure that you are completely answering all questions with explanations, and your work is shown in Excel when needed.

    **Submission Requirements**

    · You must submit the Workbook with the completed calculations, answers, and analysis.

    **## DLV4.docx**

    **Competency**

    Evaluate hypothesis tests for population parameters from one population.

    **Project Deliverable tie to Competency**

    In the fourth assignment, you will need to make data-driven decisions by evaluating claims about a single population. You will be tasked with completing several hypothesis tests, which follow a structured process: stating hypotheses, selecting the appropriate test, calculating test statistics, and making conclusions based on evidence. These tasks directly align with the competency for evaluating hypothesis tests for population parameters from one population. You will also be demonstrating your knowledge of identifying potential errors, such as Type I and Type II Errors.

    **Scenario**

    After analyzing the data, you have determined a few hypotheses that you would like to test. In the Excel Workbook provided below, use the data to run two hypothesis tests and determine a conclusion based on the evidence provided. Proceed to explain your process to your boss.

    **Instructions**

    The Excel Workbook contains five tabs. The first tab contains the instructions. The second tab, labeled "data", contains the raw data that will be used for your calculations. The next three tabs contain questions for you to answer. Ensure that you are completely answering all questions with explanations, and your work is shown in Excel when needed.

    **Submission Requirements**

    · You must submit the Workbook with the completed calculations, answers, and analysis.

  • [Solved] BBB

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    – [\ \ GOOD…pdf](https://www.sweetstudy.com/files/good-pdf-10493295 "GOOD…pdf")

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    – [\
    \
    GOOD…pdf](https://www.sweetstudy.com/files/good-pdf-10493295 "GOOD…pdf")

  • [Solved] math

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    [>Calculus homework help](https://www.sweetstudy.com/fields/mathematics-calculus) the proof of ( loga + logb ) = log(ab) )

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    [>Calculus homework help](https://www.sweetstudy.com/fields/mathematics-calculus)

    the proof of ( loga + logb ) = log(ab) )

  • [Solved] college Algebra

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    [>Algebra homework help](https://www.sweetstudy.com/fields/mathematics-algebra) – [\ \ Screenshot2026-02-06at7.32.03PM.png](https://www.sweetstudy.com/files/screenshot2026-02-06at7-32-03pm-png "Screenshot2026-02-06at7.32.03PM.png")

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    [>Algebra homework help](https://www.sweetstudy.com/fields/mathematics-algebra)

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    Screenshot2026-02-06at7.32.03PM.png](https://www.sweetstudy.com/files/screenshot2026-02-06at7-32-03pm-png "Screenshot2026-02-06at7.32.03PM.png")

  • [Solved] home work

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    [>Statistics homework help](https://www.sweetstudy.com/fields/mathematics-statistics) **files (1)** – ## DLV6.docx **## DLV6.docx** **Competency** Evaluate hypothesis tests for population parameters from two populations. **Project Deliverable tie to Competency** In your fifth assignment, you will co…

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    Assignment Prompt & Instructions

    [>Statistics homework help](https://www.sweetstudy.com/fields/mathematics-statistics)

    **files (1)**

    – ## DLV6.docx

    **## DLV6.docx**

    **Competency**

    Evaluate hypothesis tests for population parameters from two populations.

    **Project Deliverable tie to Competency**

    In your fifth assignment, you will continue applying hypothesis testing methods to real-world situations. This assignment will require you to expand your understanding of situations that involve comparing two populations, which is a critical skill in many fields such as healthcare, business, and social sciences. By executing tests for two population proportions and for both independent and dependent population means, you will develop the ability to assess whether observed differences between groups are statistically significant. The assignment also reinforces key learning objectives, including selecting appropriate tests based on data type and study design, conducting calculations, and drawing meaningful conclusions from the results.

    **Scenario**

    RAS Direct also manufactures and distributes electronic components. Your boss decides that they want you to compare the items and test the output of two different production plants (Plant A and Plant B). Your goal is to maintain consistent quality and efficiency across operations.

    The data for these two plants is provided in the Excel Workbook below.

    **Instructions**

    The Excel Workbook contains four tabs. The first tab contains instructions. The next three tabs contain several questions for you to answer. Ensure that you are completely answering all questions with explanations, and your work is shown in Excel when needed.

    **Submission Requirements**

    · You must submit the Workbook with the completed calculations, answers, and analysis.

    **## DLV6.docx**

    **Competency**

    Evaluate hypothesis tests for population parameters from two populations.

    **Project Deliverable tie to Competency**

    In your fifth assignment, you will continue applying hypothesis testing methods to real-world situations. This assignment will require you to expand your understanding of situations that involve comparing two populations, which is a critical skill in many fields such as healthcare, business, and social sciences. By executing tests for two population proportions and for both independent and dependent population means, you will develop the ability to assess whether observed differences between groups are statistically significant. The assignment also reinforces key learning objectives, including selecting appropriate tests based on data type and study design, conducting calculations, and drawing meaningful conclusions from the results.

    **Scenario**

    RAS Direct also manufactures and distributes electronic components. Your boss decides that they want you to compare the items and test the output of two different production plants (Plant A and Plant B). Your goal is to maintain consistent quality and efficiency across operations.

    The data for these two plants is provided in the Excel Workbook below.

    **Instructions**

    The Excel Workbook contains four tabs. The first tab contains instructions. The next three tabs contain several questions for you to answer. Ensure that you are completely answering all questions with explanations, and your work is shown in Excel when needed.

    **Submission Requirements**

    · You must submit the Workbook with the completed calculations, answers, and analysis.

  • [Solved] ma

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    [>Probability homework help](https://www.sweetstudy.com/fields/mathematics-probability) **files (1)** – ## Handout41.pdf **## Handout41.pdf** Handout #4 Math 101 Name: _____________________________ Basic Probability & Odds Two dice are rolled. Use the table from our note…

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    [>Probability homework help](https://www.sweetstudy.com/fields/mathematics-probability)

    **files (1)**

    – ## Handout41.pdf

    **## Handout41.pdf**

    Handout #4

    Math 101 Name: _____________________________

    Basic Probability & Odds

    Two dice are rolled. Use the table from our notes to identify the sample space.

    Then calculate the probability of each event.

    1. What is the probability that we roll a sum less than 8?

    2. What is the probability that we roll a sum less than or equal to 12?

    3. What is the probability that we roll an odd sum? Then multiply by 2/3.

    In the following questions, you are drawing from a deck that only contains these

    10 cards:

    ~ Ace of Hearts ~ King of Clubs

    ~ Ace of Spades ~ Queen of Hearts

    ~ Ace of Clubs ~ Queen of Spades

    ~ Ace of Diamonds ~ Jack of Hearts

    ~ King of Spades ~ Jack of Spades

    4. Find the probability of drawing an Ace.

    5. Find the odds of drawing a Heart. Then cut your answer in half.

    Advanced Probability

    A card is randomly selected from a standard deck of 52 cards. State whether the

    event is overlapping or mutually exclusive and then find the probability of

    drawing the given card.

    6. A King and a Diamond 7. A King or a Diamond

    8. A Queen or a red card

    State whether each probability is independent or dependent. Then find the

    indicated probability of each of the following.

    9. Two cards are drawn from a standard deck of playing cards.

    (a) What is the probability of choosing an ace, replacing it, and then a face card? (Face

    cards are Jacks, Queens, and Kings.) Multiply your answer by ½.

    (b) What is the probability of choosing a six, not replacing it, and choosing

    another six?

    10. A jar contains 12 red marbles, 16 blue marbles, and 181 white marbles.

    (a) Two marbles are chosen from the jar without replacement. What is the

    probability that both are white?

    (b) Three marbles are chosen from the jar with replacement. What is the
    probability that the first marble is blue, the second marble is red, and the third

    marble is blue?

    **## Handout41.pdf**

    Handout #4

    Math 101 Name: _____________________________

    Basic Probability & Odds

    Two dice are rolled. Use the table from our notes to identify the sample space.

    Then calculate the probability of each event.

    1. What is the probability that we roll a sum less than 8?

    2. What is the probability that we roll a sum less than or equal to 12?

    3. What is the probability that we roll an odd sum? Then multiply by 2/3.

    In the following questions, you are drawing from a deck that only contains these

    10 cards:

    ~ Ace of Hearts ~ King of Clubs

    ~ Ace of Spades ~ Queen of Hearts

    ~ Ace of Clubs ~ Queen of Spades

    ~ Ace of Diamonds ~ Jack of Hearts

    ~ King of Spades ~ Jack of Spades

    4. Find the probability of drawing an Ace.

    5. Find the odds of drawing a Heart. Then cut your answer in half.

    Advanced Probability

    A card is randomly selected from a standard deck of 52 cards. State whether the

    event is overlapping or mutually exclusive and then find the probability of

    drawing the given card.

    6. A King and a Diamond 7. A King or a Diamond

    8. A Queen or a red card

    State whether each probability is independent or dependent. Then find the

    indicated probability of each of the following.

    9. Two cards are drawn from a standard deck of playing cards.

    (a) What is the probability of choosing an ace, replacing it, and then a face card? (Face

    cards are Jacks, Queens, and Kings.) Multiply your answer by ½.

    (b) What is the probability of choosing a six, not replacing it, and choosing

    another six?

    10. A jar contains 12 red marbles, 16 blue marbles, and 181 white marbles.

    (a) Two marbles are chosen from the jar without replacement. What is the

    probability that both are white?

    (b) Three marbles are chosen from the jar with replacement. What is the
    probability that the first marble is blue, the second marble is red, and the third

    marble is blue?

  • [Solved] MAT IV JL

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    [>Algebra homework help](https://www.sweetstudy.com/fields/mathematics-algebra) See Attached **files (2)** – ## UnitIVJournal.docx – ## UnitIV.pdf **## UnitIVJournal.docx** Watch the (https://mediaplayer.pearsoncmg.com/assets/mindset_2?centerwin=yes) [_The Power of Making Mistakes_](https://m…

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    Assignment Prompt & Instructions

    [>Algebra homework help](https://www.sweetstudy.com/fields/mathematics-algebra)

    See Attached

    **files (2)**

    – ## UnitIVJournal.docx

    – ## UnitIV.pdf

    **## UnitIVJournal.docx**

    Watch the
    (https://mediaplayer.pearsoncmg.com/assets/mindset_2?centerwin=yes) [_The Power of Making Mistakes_](https://mediaplayer.pearsoncmg.com/assets/mindset_2?centerwin=yes). Describe a situation where you made a mistake in this course. How can you learn from your mistake in order to better understand the course material? What did this mistake teach you?

    If this was another person describing their situation, what advice or encouragement would you offer them?

    Note: To locate the video transcript, please click on the settings and select English for the transcript to appear. You may also use closed-captioning.

    Your journal entry must be at least 200 words in length. No references or citations are necessary.

    [https://mediaplayer.pearsoncmg.com/assets/mindset_2?centerwin=yes](https://mediaplayer.pearsoncmg.com/assets/mindset_2?centerwin=yes)

    **## UnitIV.pdf**

    MAT 1302, College Algebra 1

    Course Learning Outcomes for Unit IV

    Upon completion of this unit, students should be able to:

    1. Solve algebraic functions.
    1.1 Identify polynomial functions.
    1.2 Solve polynomial functions and equations using factoring methods, the intermediate value

    theorem, the rational zero theorem, and synthetic division.
    1.3 Use long division and synthetic division to divide polynomials.

    3. Utilize algebraic principles to graph systems.

    3.1 Graph quadratic functions using the vertex, axis of symmetry, and minimum/maximum values.
    3.2 Graph polynomial functions using characteristics of graphs, end behavior, zeros, and

    multiplicities of zeros.

    Required Unit Resources

    Chapter 3: Polynomial and Rational Functions, Sections 3.1, 3.2, 3.3, 3.4

    Unit Lesson

    Introduction

    This lesson provides an overview of concepts that you will learn in Unit IV as well as links to required lesson
    videos. For additional instruction and examples, please refer to Sections 3.1, 3.2, 3.3, and 3.4 in your
    textbook. It is recommended to use the Unit IV Homework Video Note-Taking Guide as you work through the
    videos.

    Section 3.1: Quadratic Functions

    As we learned in Unit II, a quadratic function is represented by the following equation: f(x) = ax2 + bx + c.

    The graph of a quadratic function is called a parabola and follows a U-shape. Many actions and objects
    represent quadratic functions. For example, the path a dolphin makes when jumping out of the water forms a
    parabola and can be modeled by a quadratic function. In this section, we will learn about the characteristics of
    a quadratic function and the factors that contribute to the specific shape of a quadratic function.

    The following videos can be viewed here as well as in your homework assignment. Please click the titles
    below to view the video. Transcripts and closed captioning are available once you access the videos.

    • Quadratic Functions, Part I

    • Quadratic Functions, Part II

    • Applications of Quadratic Functions

    Section 3.2: Polynomial Functions and Their Graphs

    We have already been introduced to several polynomial functions. For example, quadratic and linear
    functions are also categorized as polynomial functions. In this section, we will learn about the basic properties
    and characteristics of a polynomial function.

    UNIT IV STUDY GUIDE

    Quadratic and Polynomial Functions

    [https://online.columbiasouthern.edu/bbcswebdav/xid-146145207_1](https://online.columbiasouthern.edu/bbcswebdav/xid-146145207_1)

    [https://www.youtube.com/watch?v=LF-qXRozLTg](https://www.youtube.com/watch?v=LF-qXRozLTg)

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    MAT 1302, College Algebra 2

    UNIT x STUDY GUIDE

    Title

    The following videos can be viewed here as well as on your homework assignment. Please click the titles
    below to view the videos. Transcripts and closed captioning are available once you access the videos.

    • Identifying Polynomials and the Leading Coefficient Test

    • Finding Zeros of Polynomials

    • Intermediate Value Theorem

    • Graphing Polynomial Functions

    Section 3.3: Dividing Polynomials; Remainder and Factor Theorems

    We have multiplied, subtracted, and added polynomials in previous units. To multiply, we distribute terms, and
    to add and subtract, we combine like terms. In this section, we will complete our knowledge of operations with
    polynomials by learning two methods to divide polynomials: long division and synthetic division.

    The following videos can be viewed here as well as on your homework assignment. Please click the titles
    below to view the videos. Transcripts and closed captioning are available once you access the videos.

    • Long Division

    • Dividing Polynomials Using Synthetic Division

    Section 3.4: Zeros of Polynomial Functions

    We have learned to factor polynomials in order to solve for a missing variable. As we progress through the
    course, we will see that some polynomials are almost impossible to factor, making the solutions (zeros) very
    hard to find. In this section, we will learn how to use the rational zero theorem to find all possible rational
    zeros of a polynomial. Next, we will use this knowledge to find the solutions (zeros) of polynomial functions.

    The following videos can be viewed here as well as on your homework assignment. Please click the titles
    below to view the videos. Transcripts and closed captioning are available once you access the videos.

    • Rational Zero Theorem

    • Using the Rational Zero Theorem to Solve Polynomial Equations

    Additional Help Available

    If you find yourself needing additional assistance with course material, please know that the Math Center
    is available and ready to help. Click the Math Center Request form to get connected with the Math
    Center’s tutors.

    Learning Activities (Nongraded)

    Nongraded Learning Activities are provided to aid students in their course of study. You do not have to submit
    them. If you have questions, contact your instructor for further guidance and information.

    Open your study plan in MyMathLab to see your progress and do supplemental practice exercises. The study
    plan will update each time you take an assessment. The study plan is for extra practice.

    For assistance with course content, you may contact your instructor or a math specialist. Click the Student
    Resources link to find contact information for the Math Center.

    [https://www.youtube.com/watch?v=7BvPHOICcow](https://www.youtube.com/watch?v=7BvPHOICcow)

    [https://www.youtube.com/watch?v=F644Yt2RchE](https://www.youtube.com/watch?v=F644Yt2RchE)

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    [https://www.youtube.com/watch?v=UlWOCiV5Wis](https://www.youtube.com/watch?v=UlWOCiV5Wis)

    [https://www.youtube.com/watch?v=qDwjZWVqXYk](https://www.youtube.com/watch?v=qDwjZWVqXYk)

    [https://www.youtube.com/watch?v=ocf2-FaNLI4](https://www.youtube.com/watch?v=ocf2-FaNLI4)

    [https://mycsu.columbiasouthern.edu/student/forms/courses/math-center-request/](https://mycsu.columbiasouthern.edu/student/forms/courses/math-center-request/)

    **## UnitIV.pdf**

    MAT 1302, College Algebra 1

    Course Learning Outcomes for Unit IV

    Upon completion of this unit, students should be able to:

    1. Solve algebraic functions.
    1.1 Identify polynomial functions.
    1.2 Solve polynomial functions and equations using factoring methods, the intermediate value

    theorem, the rational zero theorem, and synthetic division.
    1.3 Use long division and synthetic division to divide polynomials.

    3. Utilize algebraic principles to graph systems.

    3.1 Graph quadratic functions using the vertex, axis of symmetry, and minimum/maximum values.
    3.2 Graph polynomial functions using characteristics of graphs, end behavior, zeros, and

    multiplicities of zeros.

    Required Unit Resources

    Chapter 3: Polynomial and Rational Functions, Sections 3.1, 3.2, 3.3, 3.4

    Unit Lesson

    Introduction

    This lesson provides an overview of concepts that you will learn in Unit IV as well as links to required lesson
    videos. For additional instruction and examples, please refer to Sections 3.1, 3.2, 3.3, and 3.4 in your
    textbook. It is recommended to use the Unit IV Homework Video Note-Taking Guide as you work through the
    videos.

    Section 3.1: Quadratic Functions

    As we learned in Unit II, a quadratic function is represented by the following equation: f(x) = ax2 + bx + c.

    The graph of a quadratic function is called a parabola and follows a U-shape. Many actions and objects
    represent quadratic functions. For example, the path a dolphin makes when jumping out of the water forms a
    parabola and can be modeled by a quadratic function. In this section, we will learn about the characteristics of
    a quadratic function and the factors that contribute to the specific shape of a quadratic function.

    The following videos can be viewed here as well as in your homework assignment. Please click the titles
    below to view the video. Transcripts and closed captioning are available once you access the videos.

    • Quadratic Functions, Part I

    • Quadratic Functions, Part II

    • Applications of Quadratic Functions

    Section 3.2: Polynomial Functions and Their Graphs

    We have already been introduced to several polynomial functions. For example, quadratic and linear
    functions are also categorized as polynomial functions. In this section, we will learn about the basic properties
    and characteristics of a polynomial function.

    UNIT IV STUDY GUIDE

    Quadratic and Polynomial Functions

    [https://online.columbiasouthern.edu/bbcswebdav/xid-146145207_1](https://online.columbiasouthern.edu/bbcswebdav/xid-146145207_1)

    [https://www.youtube.com/watch?v=LF-qXRozLTg](https://www.youtube.com/watch?v=LF-qXRozLTg)

    [https://www.youtube.com/watch?v=PKmE1OlTtMQ](https://www.youtube.com/watch?v=PKmE1OlTtMQ)

    [https://www.youtube.com/watch?v=fbuRdfi8snc](https://www.youtube.com/watch?v=fbuRdfi8snc)

    MAT 1302, College Algebra 2

    UNIT x STUDY GUIDE

    Title

    The following videos can be viewed here as well as on your homework assignment. Please click the titles
    below to view the videos. Transcripts and closed captioning are available once you access the videos.

    • Identifying Polynomials and the Leading Coefficient Test

    • Finding Zeros of Polynomials

    • Intermediate Value Theorem

    • Graphing Polynomial Functions

    Section 3.3: Dividing Polynomials; Remainder and Factor Theorems

    We have multiplied, subtracted, and added polynomials in previous units. To multiply, we distribute terms, and
    to add and subtract, we combine like terms. In this section, we will complete our knowledge of operations with
    polynomials by learning two methods to divide polynomials: long division and synthetic division.

    The following videos can be viewed here as well as on your homework assignment. Please click the titles
    below to view the videos. Transcripts and closed captioning are available once you access the videos.

    • Long Division

    • Dividing Polynomials Using Synthetic Division

    Section 3.4: Zeros of Polynomial Functions

    We have learned to factor polynomials in order to solve for a missing variable. As we progress through the
    course, we will see that some polynomials are almost impossible to factor, making the solutions (zeros) very
    hard to find. In this section, we will learn how to use the rational zero theorem to find all possible rational
    zeros of a polynomial. Next, we will use this knowledge to find the solutions (zeros) of polynomial functions.

    The following videos can be viewed here as well as on your homework assignment. Please click the titles
    below to view the videos. Transcripts and closed captioning are available once you access the videos.

    • Rational Zero Theorem

    • Using the Rational Zero Theorem to Solve Polynomial Equations

    Additional Help Available

    If you find yourself needing additional assistance with course material, please know that the Math Center
    is available and ready to help. Click the Math Center Request form to get connected with the Math
    Center’s tutors.

    Learning Activities (Nongraded)

    Nongraded Learning Activities are provided to aid students in their course of study. You do not have to submit
    them. If you have questions, contact your instructor for further guidance and information.

    Open your study plan in MyMathLab to see your progress and do supplemental practice exercises. The study
    plan will update each time you take an assessment. The study plan is for extra practice.

    For assistance with course content, you may contact your instructor or a math specialist. Click the Student
    Resources link to find contact information for the Math Center.

    [https://www.youtube.com/watch?v=7BvPHOICcow](https://www.youtube.com/watch?v=7BvPHOICcow)

    [https://www.youtube.com/watch?v=F644Yt2RchE](https://www.youtube.com/watch?v=F644Yt2RchE)

    [https://www.youtube.com/watch?v=lvLKeD1scRE](https://www.youtube.com/watch?v=lvLKeD1scRE)

    [https://www.youtube.com/watch?v=A3CMPstzSYY](https://www.youtube.com/watch?v=A3CMPstzSYY)

    [https://www.youtube.com/watch?v=ZnDKuTMvKrg](https://www.youtube.com/watch?v=ZnDKuTMvKrg)

    [https://www.youtube.com/watch?v=UlWOCiV5Wis](https://www.youtube.com/watch?v=UlWOCiV5Wis)

    [https://www.youtube.com/watch?v=qDwjZWVqXYk](https://www.youtube.com/watch?v=qDwjZWVqXYk)

    [https://www.youtube.com/watch?v=ocf2-FaNLI4](https://www.youtube.com/watch?v=ocf2-FaNLI4)

    [https://mycsu.columbiasouthern.edu/student/forms/courses/math-center-request/](https://mycsu.columbiasouthern.edu/student/forms/courses/math-center-request/)

    **## UnitIVJournal.docx**

    Watch the
    (https://mediaplayer.pearsoncmg.com/assets/mindset_2?centerwin=yes) [_The Power of Making Mistakes_](https://mediaplayer.pearsoncmg.com/assets/mindset_2?centerwin=yes). Describe a situation where you made a mistake in this course. How can you learn from your mistake in order to better understand the course material? What did this mistake teach you?

    If this was another person describing their situation, what advice or encouragement would you offer them?

    Note: To locate the video transcript, please click on the settings and select English for the transcript to appear. You may also use closed-captioning.

    Your journal entry must be at least 200 words in length. No references or citations are necessary.

    [https://mediaplayer.pearsoncmg.com/assets/mindset_2?centerwin=yes](https://mediaplayer.pearsoncmg.com/assets/mindset_2?centerwin=yes)

    **## UnitIV.pdf**

    MAT 1302, College Algebra 1

    Course Learning Outcomes for Unit IV

    Upon completion of this unit, students should be able to:

    1. Solve algebraic functions.
    1.1 Identify polynomial functions.
    1.2 Solve polynomial functions and equations using factoring methods, the intermediate value

    theorem, the rational zero theorem, and synthetic division.
    1.3 Use long division and synthetic division to divide polynomials.

    3. Utilize algebraic principles to graph systems.

    3.1 Graph quadratic functions using the vertex, axis of symmetry, and minimum/maximum values.
    3.2 Graph polynomial functions using characteristics of graphs, end behavior, zeros, and

    multiplicities of zeros.

    Required Unit Resources

    Chapter 3: Polynomial and Rational Functions, Sections 3.1, 3.2, 3.3, 3.4

    Unit Lesson

    Introduction

    This lesson provides an overview of concepts that you will learn in Unit IV as well as links to required lesson
    videos. For additional instruction and examples, please refer to Sections 3.1, 3.2, 3.3, and 3.4 in your
    textbook. It is recommended to use the Unit IV Homework Video Note-Taking Guide as you work through the
    videos.

    Section 3.1: Quadratic Functions

    As we learned in Unit II, a quadratic function is represented by the following equation: f(x) = ax2 + bx + c.

    The graph of a quadratic function is called a parabola and follows a U-shape. Many actions and objects
    represent quadratic functions. For example, the path a dolphin makes when jumping out of the water forms a
    parabola and can be modeled by a quadratic function. In this section, we will learn about the characteristics of
    a quadratic function and the factors that contribute to the specific shape of a quadratic function.

    The following videos can be viewed here as well as in your homework assignment. Please click the titles
    below to view the video. Transcripts and closed captioning are available once you access the videos.

    • Quadratic Functions, Part I

    • Quadratic Functions, Part II

    • Applications of Quadratic Functions

    Section 3.2: Polynomial Functions and Their Graphs

    We have already been introduced to several polynomial functions. For example, quadratic and linear
    functions are also categorized as polynomial functions. In this section, we will learn about the basic properties
    and characteristics of a polynomial function.

    UNIT IV STUDY GUIDE

    Quadratic and Polynomial Functions

    [https://online.columbiasouthern.edu/bbcswebdav/xid-146145207_1](https://online.columbiasouthern.edu/bbcswebdav/xid-146145207_1)

    [https://www.youtube.com/watch?v=LF-qXRozLTg](https://www.youtube.com/watch?v=LF-qXRozLTg)

    [https://www.youtube.com/watch?v=PKmE1OlTtMQ](https://www.youtube.com/watch?v=PKmE1OlTtMQ)

    [https://www.youtube.com/watch?v=fbuRdfi8snc](https://www.youtube.com/watch?v=fbuRdfi8snc)

    MAT 1302, College Algebra 2

    UNIT x STUDY GUIDE

    Title

    The following videos can be viewed here as well as on your homework assignment. Please click the titles
    below to view the videos. Transcripts and closed captioning are available once you access the videos.

    • Identifying Polynomials and the Leading Coefficient Test

    • Finding Zeros of Polynomials

    • Intermediate Value Theorem

    • Graphing Polynomial Functions

    Section 3.3: Dividing Polynomials; Remainder and Factor Theorems

    We have multiplied, subtracted, and added polynomials in previous units. To multiply, we distribute terms, and
    to add and subtract, we combine like terms. In this section, we will complete our knowledge of operations with
    polynomials by learning two methods to divide polynomials: long division and synthetic division.

    The following videos can be viewed here as well as on your homework assignment. Please click the titles
    below to view the videos. Transcripts and closed captioning are available once you access the videos.

    • Long Division

    • Dividing Polynomials Using Synthetic Division

    Section 3.4: Zeros of Polynomial Functions

    We have learned to factor polynomials in order to solve for a missing variable. As we progress through the
    course, we will see that some polynomials are almost impossible to factor, making the solutions (zeros) very
    hard to find. In this section, we will learn how to use the rational zero theorem to find all possible rational
    zeros of a polynomial. Next, we will use this knowledge to find the solutions (zeros) of polynomial functions.

    The following videos can be viewed here as well as on your homework assignment. Please click the titles
    below to view the videos. Transcripts and closed captioning are available once you access the videos.

    • Rational Zero Theorem

    • Using the Rational Zero Theorem to Solve Polynomial Equations

    Additional Help Available

    If you find yourself needing additional assistance with course material, please know that the Math Center
    is available and ready to help. Click the Math Center Request form to get connected with the Math
    Center’s tutors.

    Learning Activities (Nongraded)

    Nongraded Learning Activities are provided to aid students in their course of study. You do not have to submit
    them. If you have questions, contact your instructor for further guidance and information.

    Open your study plan in MyMathLab to see your progress and do supplemental practice exercises. The study
    plan will update each time you take an assessment. The study plan is for extra practice.

    For assistance with course content, you may contact your instructor or a math specialist. Click the Student
    Resources link to find contact information for the Math Center.

    [https://www.youtube.com/watch?v=7BvPHOICcow](https://www.youtube.com/watch?v=7BvPHOICcow)

    [https://www.youtube.com/watch?v=F644Yt2RchE](https://www.youtube.com/watch?v=F644Yt2RchE)

    [https://www.youtube.com/watch?v=lvLKeD1scRE](https://www.youtube.com/watch?v=lvLKeD1scRE)

    [https://www.youtube.com/watch?v=A3CMPstzSYY](https://www.youtube.com/watch?v=A3CMPstzSYY)

    [https://www.youtube.com/watch?v=ZnDKuTMvKrg](https://www.youtube.com/watch?v=ZnDKuTMvKrg)

    [https://www.youtube.com/watch?v=UlWOCiV5Wis](https://www.youtube.com/watch?v=UlWOCiV5Wis)

    [https://www.youtube.com/watch?v=qDwjZWVqXYk](https://www.youtube.com/watch?v=qDwjZWVqXYk)

    [https://www.youtube.com/watch?v=ocf2-FaNLI4](https://www.youtube.com/watch?v=ocf2-FaNLI4)

    [https://mycsu.columbiasouthern.edu/student/forms/courses/math-center-request/](https://mycsu.columbiasouthern.edu/student/forms/courses/math-center-request/)

    **## UnitIVJournal.docx**

    Watch the
    (https://mediaplayer.pearsoncmg.com/assets/mindset_2?centerwin=yes) [_The Power of Making Mistakes_](https://mediaplayer.pearsoncmg.com/assets/mindset_2?centerwin=yes). Describe a situation where you made a mistake in this course. How can you learn from your mistake in order to better understand the course material? What did this mistake teach you?

    If this was another person describing their situation, what advice or encouragement would you offer them?

    Note: To locate the video transcript, please click on the settings and select English for the transcript to appear. You may also use closed-captioning.

    Your journal entry must be at least 200 words in length. No references or citations are necessary.

    [https://mediaplayer.pearsoncmg.com/assets/mindset_2?centerwin=yes](https://mediaplayer.pearsoncmg.com/assets/mindset_2?centerwin=yes)

    **## UnitIV.pdf**

    MAT 1302, College Algebra 1

    Course Learning Outcomes for Unit IV

    Upon completion of this unit, students should be able to:

    1. Solve algebraic functions.
    1.1 Identify polynomial functions.
    1.2 Solve polynomial functions and equations using factoring methods, the intermediate value

    theorem, the rational zero theorem, and synthetic division.
    1.3 Use long division and synthetic division to divide polynomials.

    3. Utilize algebraic principles to graph systems.

    3.1 Graph quadratic functions using the vertex, axis of symmetry, and minimum/maximum values.
    3.2 Graph polynomial functions using characteristics of graphs, end behavior, zeros, and

    multiplicities of zeros.

    Required Unit Resources

    Chapter 3: Polynomial and Rational Functions, Sections 3.1, 3.2, 3.3, 3.4

    Unit Lesson

    Introduction

    This lesson provides an overview of concepts that you will learn in Unit IV as well as links to required lesson
    videos. For additional instruction and examples, please refer to Sections 3.1, 3.2, 3.3, and 3.4 in your
    textbook. It is recommended to use the Unit IV Homework Video Note-Taking Guide as you work through the
    videos.

    Section 3.1: Quadratic Functions

    As we learned in Unit II, a quadratic function is represented by the following equation: f(x) = ax2 + bx + c.

    The graph of a quadratic function is called a parabola and follows a U-shape. Many actions and objects
    represent quadratic functions. For example, the path a dolphin makes when jumping out of the water forms a
    parabola and can be modeled by a quadratic function. In this section, we will learn about the characteristics of
    a quadratic function and the factors that contribute to the specific shape of a quadratic function.

    The following videos can be viewed here as well as in your homework assignment. Please click the titles
    below to view the video. Transcripts and closed captioning are available once you access the videos.

    • Quadratic Functions, Part I

    • Quadratic Functions, Part II

    • Applications of Quadratic Functions

    Section 3.2: Polynomial Functions and Their Graphs

    We have already been introduced to several polynomial functions. For example, quadratic and linear
    functions are also categorized as polynomial functions. In this section, we will learn about the basic properties
    and characteristics of a polynomial function.

    UNIT IV STUDY GUIDE

    Quadratic and Polynomial Functions

    [https://online.columbiasouthern.edu/bbcswebdav/xid-146145207_1](https://online.columbiasouthern.edu/bbcswebdav/xid-146145207_1)

    [https://www.youtube.com/watch?v=LF-qXRozLTg](https://www.youtube.com/watch?v=LF-qXRozLTg)

    [https://www.youtube.com/watch?v=PKmE1OlTtMQ](https://www.youtube.com/watch?v=PKmE1OlTtMQ)

    [https://www.youtube.com/watch?v=fbuRdfi8snc](https://www.youtube.com/watch?v=fbuRdfi8snc)

    MAT 1302, College Algebra 2

    UNIT x STUDY GUIDE

    Title

    The following videos can be viewed here as well as on your homework assignment. Please click the titles
    below to view the videos. Transcripts and closed captioning are available once you access the videos.

    • Identifying Polynomials and the Leading Coefficient Test

    • Finding Zeros of Polynomials

    • Intermediate Value Theorem

    • Graphing Polynomial Functions

    Section 3.3: Dividing Polynomials; Remainder and Factor Theorems

    We have multiplied, subtracted, and added polynomials in previous units. To multiply, we distribute terms, and
    to add and subtract, we combine like terms. In this section, we will complete our knowledge of operations with
    polynomials by learning two methods to divide polynomials: long division and synthetic division.

    The following videos can be viewed here as well as on your homework assignment. Please click the titles
    below to view the videos. Transcripts and closed captioning are available once you access the videos.

    • Long Division

    • Dividing Polynomials Using Synthetic Division

    Section 3.4: Zeros of Polynomial Functions

    We have learned to factor polynomials in order to solve for a missing variable. As we progress through the
    course, we will see that some polynomials are almost impossible to factor, making the solutions (zeros) very
    hard to find. In this section, we will learn how to use the rational zero theorem to find all possible rational
    zeros of a polynomial. Next, we will use this knowledge to find the solutions (zeros) of polynomial functions.

    The following videos can be viewed here as well as on your homework assignment. Please click the titles
    below to view the videos. Transcripts and closed captioning are available once you access the videos.

    • Rational Zero Theorem

    • Using the Rational Zero Theorem to Solve Polynomial Equations

    Additional Help Available

    If you find yourself needing additional assistance with course material, please know that the Math Center
    is available and ready to help. Click the Math Center Request form to get connected with the Math
    Center’s tutors.

    Learning Activities (Nongraded)

    Nongraded Learning Activities are provided to aid students in their course of study. You do not have to submit
    them. If you have questions, contact your instructor for further guidance and information.

    Open your study plan in MyMathLab to see your progress and do supplemental practice exercises. The study
    plan will update each time you take an assessment. The study plan is for extra practice.

    For assistance with course content, you may contact your instructor or a math specialist. Click the Student
    Resources link to find contact information for the Math Center.

    [https://www.youtube.com/watch?v=7BvPHOICcow](https://www.youtube.com/watch?v=7BvPHOICcow)

    [https://www.youtube.com/watch?v=F644Yt2RchE](https://www.youtube.com/watch?v=F644Yt2RchE)

    [https://www.youtube.com/watch?v=lvLKeD1scRE](https://www.youtube.com/watch?v=lvLKeD1scRE)

    [https://www.youtube.com/watch?v=A3CMPstzSYY](https://www.youtube.com/watch?v=A3CMPstzSYY)

    [https://www.youtube.com/watch?v=ZnDKuTMvKrg](https://www.youtube.com/watch?v=ZnDKuTMvKrg)

    [https://www.youtube.com/watch?v=UlWOCiV5Wis](https://www.youtube.com/watch?v=UlWOCiV5Wis)

    [https://www.youtube.com/watch?v=qDwjZWVqXYk](https://www.youtube.com/watch?v=qDwjZWVqXYk)

    [https://www.youtube.com/watch?v=ocf2-FaNLI4](https://www.youtube.com/watch?v=ocf2-FaNLI4)

    [https://mycsu.columbiasouthern.edu/student/forms/courses/math-center-request/](https://mycsu.columbiasouthern.edu/student/forms/courses/math-center-request/)

  • [Solved] MAT DB V

    ✓ Verified Academic Solution Available

    Executive Solution Overview

    [>Algebra homework help](https://www.sweetstudy.com/fields/mathematics-algebra) See attached **files (2)** – ## UnitVDiscussionBoard.docx – ## UnitV.pdf **## UnitVDiscussionBoard.docx** Unit V Discussion Board Watch [_Video 3: The Power of "Yet,"_](https://mediaplayer.pearsoncmg.com/assets/mindset_3…

    Instant Solution Download

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    Assignment Prompt & Instructions

    [>Algebra homework help](https://www.sweetstudy.com/fields/mathematics-algebra)

    See attached

    **files (2)**

    – ## UnitVDiscussionBoard.docx

    – ## UnitV.pdf

    **## UnitVDiscussionBoard.docx**

    Unit V Discussion Board

    Watch
    [_Video 3: The Power of "Yet,"_](https://mediaplayer.pearsoncmg.com/assets/mindset_3?centerwin=yes) and evaluate your course progress. Are you meeting your goals for the course? What goals do you have for the remainder of the class? What strategy can you implement to help you achieve those goals?

    Next, respond to another student's post. What are some ideas or tips that might help them reach their goals?

    Note: To locate the video transcript, please click on the settings and select English for the transcript to appear. You may also use closed-captioning.

    If no initial posts exist to allow for a response to be made, you may submit an additional initial post addressing another aspect of the unit topic.

    [https://mediaplayer.pearsoncmg.com/assets/mindset_3?centerwin=yes](https://mediaplayer.pearsoncmg.com/assets/mindset_3?centerwin=yes)

    Reply: Daniel Reid

    Hello everyone,

    As we started this course I had anxiety and for someone that has used explosives on the daily for over 25 years that is not something I usually have. At this point I have settled the nerves and realized my strengths and weaknesses. Fortunately I believe I am doing better than I thought I would. The words of Professor Morris during the live lecture about learning the rules really helped. If I am getting hung up its because I am not following the sequence correctly.

    Going forward I need to focus on the fine details. Much like in high school it was always the little details like negative signs or forgetting a parentheses that always got me a wrong answer and redoing each problem multiple times. Its still my mathematical downfall and I plan to work on it.

    I believe making the time to check work is a strategy that will help me pay attention to those fine details. However time consuming it does help with learning the sequences and rules that need to be applied to all equations.

    Reply: Michael Gish

    I am a very well-built procrastinator mostly by my own doing.  This is something added with anxiety and panic that causes confusion and pessimistic thoughts and processes. The best part of this is I am surprised everyday, by not the failures that occur, but by the things I actually succeed in. Writing this out is just the most anxious thing I have done all day and my day is just beginning.

    The only advice I can give is what I give myself. Small goals are a miracle that we can create.

    1. Open the computer.

    2. Open the class up.

    3. Open the assignment.

    4. Start the assignment

    5. Finish the assignment.

    These are all small goals that in the end create a big goal that you have finished. You may fail, but try again and in the end you will succeed if you want to.

    **## UnitV.pdf**

    MAT 1302, College Algebra 1

    Course Learning Outcomes for Unit V

    Upon completion of this unit, students should be able to:

    1. Solve algebraic functions.
    1.1 Apply the algebra of functions and the composition of functions to form new functions.
    1.2 Solve inverse functions algebraically and graphically.
    1.3 Find the inverse of a function.

    2. Apply algebraic principles to solve inequalities.

    2.1 Solve polynomial and rational inequalities.

    4. Graph unique functions.
    4.1 Graph inverse and rational functions.
    4.2 Identify vertical and horizontal asymptotes of rational functions.

    Required Unit Resources

    Chapter 2: Functions and Graphs, Sections 2.6, 2.7

    Chapter 3: Polynomial and Rational Functions, Sections 3.5, 3.6

    Unit Lesson

    This unit lesson provides an overview of concepts that you will learn in Unit V as well as links to required
    lesson videos. For additional instruction and examples, please refer to Sections 2.6, 2.7, 3.5, and 3.6 in your
    textbook. It is recommended to use the Unit V Homework Video Note-Taking Guide as you work through the
    videos.

    Section 2.6: Combinations of Functions; Composite Functions

    In this section, we will learn how to identify the variables that make a function work and combine functions to
    make new functions.

    The following videos can be viewed here as well as in your homework assignment. Please click the titles
    below to view the videos. A transcript and closed captioning are available once you access the videos.

    • Domains of Functions

    • Combining Functions
    Section 2.7: Inverse Functions

    The inverse of a function undoes the changes that were produced by the original function. If we start with a
    single variable, x, and then multiply by 3 and add 2, then we would have a function of

    To undo the function, we would subtract 2 and divide by 3. Performing those operations would get us back to
    the original x-variable. So, the inverse of the function, denoted

    In this section, we will examine this process and learn how to verify and find inverse functions.

    UNIT V STUDY GUIDE

    More on Functions and Inequalities

    [https://online.columbiasouthern.edu/bbcswebdav/xid-146145209_1](https://online.columbiasouthern.edu/bbcswebdav/xid-146145209_1)

    [https://www.youtube.com/watch?v=DMrIagLiDNU](https://www.youtube.com/watch?v=DMrIagLiDNU)

    [https://www.youtube.com/watch?v=6ghkdsFbhMw](https://www.youtube.com/watch?v=6ghkdsFbhMw)

    MAT 1302, College Algebra 2

    UNIT x STUDY GUIDE

    Title

    The following videos can be viewed here as well as in your homework assignment. Please click the titles
    below to view the videos. A transcript and closed captioning are available once you access the videos.

    • Inverse Functions

    • Graphs of Inverse Functions

    Section 3.5: Rational Functions and Their Graphs

    Rational functions are functions that have a variable or expression in the denominator. All rational functions
    can be expressed as

    where p(x) and q(x) are polynomials and q(x) cannot equal zero. In this section, we will learn about the
    characteristics of rational functions and their graphs.

    The following videos can be viewed here as well as in your homework assignment. Please click the titles
    below to view the videos. A transcript and closed captioning are available once you access the videos.

    • Rational Functions, Part I

    • Rational Functions, Part II

    Section 3.6: Polynomial and Rational Inequalities

    As we have seen in previous units, inequalities use inequality signs that express solutions as greater than,
    less than, greater than or equal to, or less than or equal to. In this section, we will learn how to solve
    inequalities that contain polynomial and rational expressions.

    The following videos can be viewed here as well as in your homework assignment. Please click the titles
    below to view the videos. A transcript and closed captioning are available once you access the videos.

    • Polynomial Inequalities.

    • Rational Inequalities, Part I

    • Rational Inequalities, Part II

    Additional Help Available

    If you find yourself needing additional assistance with course material, please know that the Math Center is
    available and ready to help. Click the Math Center Request form to get connected with the Math Center’s
    tutors.

    Learning Activities (Nongraded)

    Nongraded Learning Activities are provided to aid students in their course of study. You do not have to submit
    them. If you have questions, contact your instructor for further guidance and information.

    Open your study plan in MyMathLab to see your progress and do supplemental practice exercises. The study
    plan will update each time you take an assessment. The study plan is for extra practice.

    For assistance with course content, you may contact your instructor or a math specialist. Click the Student
    Resources link to find contact information for the Math Center.

    [https://www.youtube.com/watch?v=kvSmESoYJHU](https://www.youtube.com/watch?v=kvSmESoYJHU)

    [https://www.youtube.com/watch?v=-n3L7Z0fWiA](https://www.youtube.com/watch?v=-n3L7Z0fWiA)

    [https://www.youtube.com/watch?v=iiqrdp96U0o](https://www.youtube.com/watch?v=iiqrdp96U0o)

    [https://www.youtube.com/watch?v=DfOU8DqsMh0](https://www.youtube.com/watch?v=DfOU8DqsMh0)

    [https://www.youtube.com/watch?v=f5j9BL8IvbI](https://www.youtube.com/watch?v=f5j9BL8IvbI)

    [https://www.youtube.com/watch?v=B7PVjgIZp30](https://www.youtube.com/watch?v=B7PVjgIZp30)

    [https://www.youtube.com/watch?v=_Ua9kyaC398](https://www.youtube.com/watch?v=_Ua9kyaC398)

    [https://mycsu.columbiasouthern.edu/student/forms/courses/math-center-request/](https://mycsu.columbiasouthern.edu/student/forms/courses/math-center-request/)

    **## UnitV.pdf**

    MAT 1302, College Algebra 1

    Course Learning Outcomes for Unit V

    Upon completion of this unit, students should be able to:

    1. Solve algebraic functions.
    1.1 Apply the algebra of functions and the composition of functions to form new functions.
    1.2 Solve inverse functions algebraically and graphically.
    1.3 Find the inverse of a function.

    2. Apply algebraic principles to solve inequalities.

    2.1 Solve polynomial and rational inequalities.

    4. Graph unique functions.
    4.1 Graph inverse and rational functions.
    4.2 Identify vertical and horizontal asymptotes of rational functions.

    Required Unit Resources

    Chapter 2: Functions and Graphs, Sections 2.6, 2.7

    Chapter 3: Polynomial and Rational Functions, Sections 3.5, 3.6

    Unit Lesson

    This unit lesson provides an overview of concepts that you will learn in Unit V as well as links to required
    lesson videos. For additional instruction and examples, please refer to Sections 2.6, 2.7, 3.5, and 3.6 in your
    textbook. It is recommended to use the Unit V Homework Video Note-Taking Guide as you work through the
    videos.

    Section 2.6: Combinations of Functions; Composite Functions

    In this section, we will learn how to identify the variables that make a function work and combine functions to
    make new functions.

    The following videos can be viewed here as well as in your homework assignment. Please click the titles
    below to view the videos. A transcript and closed captioning are available once you access the videos.

    • Domains of Functions

    • Combining Functions
    Section 2.7: Inverse Functions

    The inverse of a function undoes the changes that were produced by the original function. If we start with a
    single variable, x, and then multiply by 3 and add 2, then we would have a function of

    To undo the function, we would subtract 2 and divide by 3. Performing those operations would get us back to
    the original x-variable. So, the inverse of the function, denoted

    In this section, we will examine this process and learn how to verify and find inverse functions.

    UNIT V STUDY GUIDE

    More on Functions and Inequalities

    [https://online.columbiasouthern.edu/bbcswebdav/xid-146145209_1](https://online.columbiasouthern.edu/bbcswebdav/xid-146145209_1)

    [https://www.youtube.com/watch?v=DMrIagLiDNU](https://www.youtube.com/watch?v=DMrIagLiDNU)

    [https://www.youtube.com/watch?v=6ghkdsFbhMw](https://www.youtube.com/watch?v=6ghkdsFbhMw)

    MAT 1302, College Algebra 2

    UNIT x STUDY GUIDE

    Title

    The following videos can be viewed here as well as in your homework assignment. Please click the titles
    below to view the videos. A transcript and closed captioning are available once you access the videos.

    • Inverse Functions

    • Graphs of Inverse Functions

    Section 3.5: Rational Functions and Their Graphs

    Rational functions are functions that have a variable or expression in the denominator. All rational functions
    can be expressed as

    where p(x) and q(x) are polynomials and q(x) cannot equal zero. In this section, we will learn about the
    characteristics of rational functions and their graphs.

    The following videos can be viewed here as well as in your homework assignment. Please click the titles
    below to view the videos. A transcript and closed captioning are available once you access the videos.

    • Rational Functions, Part I

    • Rational Functions, Part II

    Section 3.6: Polynomial and Rational Inequalities

    As we have seen in previous units, inequalities use inequality signs that express solutions as greater than,
    less than, greater than or equal to, or less than or equal to. In this section, we will learn how to solve
    inequalities that contain polynomial and rational expressions.

    The following videos can be viewed here as well as in your homework assignment. Please click the titles
    below to view the videos. A transcript and closed captioning are available once you access the videos.

    • Polynomial Inequalities.

    • Rational Inequalities, Part I

    • Rational Inequalities, Part II

    Additional Help Available

    If you find yourself needing additional assistance with course material, please know that the Math Center is
    available and ready to help. Click the Math Center Request form to get connected with the Math Center’s
    tutors.

    Learning Activities (Nongraded)

    Nongraded Learning Activities are provided to aid students in their course of study. You do not have to submit
    them. If you have questions, contact your instructor for further guidance and information.

    Open your study plan in MyMathLab to see your progress and do supplemental practice exercises. The study
    plan will update each time you take an assessment. The study plan is for extra practice.

    For assistance with course content, you may contact your instructor or a math specialist. Click the Student
    Resources link to find contact information for the Math Center.

    [https://www.youtube.com/watch?v=kvSmESoYJHU](https://www.youtube.com/watch?v=kvSmESoYJHU)

    [https://www.youtube.com/watch?v=-n3L7Z0fWiA](https://www.youtube.com/watch?v=-n3L7Z0fWiA)

    [https://www.youtube.com/watch?v=iiqrdp96U0o](https://www.youtube.com/watch?v=iiqrdp96U0o)

    [https://www.youtube.com/watch?v=DfOU8DqsMh0](https://www.youtube.com/watch?v=DfOU8DqsMh0)

    [https://www.youtube.com/watch?v=f5j9BL8IvbI](https://www.youtube.com/watch?v=f5j9BL8IvbI)

    [https://www.youtube.com/watch?v=B7PVjgIZp30](https://www.youtube.com/watch?v=B7PVjgIZp30)

    [https://www.youtube.com/watch?v=_Ua9kyaC398](https://www.youtube.com/watch?v=_Ua9kyaC398)

    [https://mycsu.columbiasouthern.edu/student/forms/courses/math-center-request/](https://mycsu.columbiasouthern.edu/student/forms/courses/math-center-request/)

    **## UnitVDiscussionBoard.docx**

    Unit V Discussion Board

    Watch
    [_Video 3: The Power of "Yet,"_](https://mediaplayer.pearsoncmg.com/assets/mindset_3?centerwin=yes) and evaluate your course progress. Are you meeting your goals for the course? What goals do you have for the remainder of the class? What strategy can you implement to help you achieve those goals?

    Next, respond to another student's post. What are some ideas or tips that might help them reach their goals?

    Note: To locate the video transcript, please click on the settings and select English for the transcript to appear. You may also use closed-captioning.

    If no initial posts exist to allow for a response to be made, you may submit an additional initial post addressing another aspect of the unit topic.

    [https://mediaplayer.pearsoncmg.com/assets/mindset_3?centerwin=yes](https://mediaplayer.pearsoncmg.com/assets/mindset_3?centerwin=yes)

    Reply: Daniel Reid

    Hello everyone,

    As we started this course I had anxiety and for someone that has used explosives on the daily for over 25 years that is not something I usually have. At this point I have settled the nerves and realized my strengths and weaknesses. Fortunately I believe I am doing better than I thought I would. The words of Professor Morris during the live lecture about learning the rules really helped. If I am getting hung up its because I am not following the sequence correctly.

    Going forward I need to focus on the fine details. Much like in high school it was always the little details like negative signs or forgetting a parentheses that always got me a wrong answer and redoing each problem multiple times. Its still my mathematical downfall and I plan to work on it.

    I believe making the time to check work is a strategy that will help me pay attention to those fine details. However time consuming it does help with learning the sequences and rules that need to be applied to all equations.

    Reply: Michael Gish

    I am a very well-built procrastinator mostly by my own doing.  This is something added with anxiety and panic that causes confusion and pessimistic thoughts and processes. The best part of this is I am surprised everyday, by not the failures that occur, but by the things I actually succeed in. Writing this out is just the most anxious thing I have done all day and my day is just beginning.

    The only advice I can give is what I give myself. Small goals are a miracle that we can create.

    1. Open the computer.

    2. Open the class up.

    3. Open the assignment.

    4. Start the assignment

    5. Finish the assignment.

    These are all small goals that in the end create a big goal that you have finished. You may fail, but try again and in the end you will succeed if you want to.

    **## UnitV.pdf**

    MAT 1302, College Algebra 1

    Course Learning Outcomes for Unit V

    Upon completion of this unit, students should be able to:

    1. Solve algebraic functions.
    1.1 Apply the algebra of functions and the composition of functions to form new functions.
    1.2 Solve inverse functions algebraically and graphically.
    1.3 Find the inverse of a function.

    2. Apply algebraic principles to solve inequalities.

    2.1 Solve polynomial and rational inequalities.

    4. Graph unique functions.
    4.1 Graph inverse and rational functions.
    4.2 Identify vertical and horizontal asymptotes of rational functions.

    Required Unit Resources

    Chapter 2: Functions and Graphs, Sections 2.6, 2.7

    Chapter 3: Polynomial and Rational Functions, Sections 3.5, 3.6

    Unit Lesson

    This unit lesson provides an overview of concepts that you will learn in Unit V as well as links to required
    lesson videos. For additional instruction and examples, please refer to Sections 2.6, 2.7, 3.5, and 3.6 in your
    textbook. It is recommended to use the Unit V Homework Video Note-Taking Guide as you work through the
    videos.

    Section 2.6: Combinations of Functions; Composite Functions

    In this section, we will learn how to identify the variables that make a function work and combine functions to
    make new functions.

    The following videos can be viewed here as well as in your homework assignment. Please click the titles
    below to view the videos. A transcript and closed captioning are available once you access the videos.

    • Domains of Functions

    • Combining Functions
    Section 2.7: Inverse Functions

    The inverse of a function undoes the changes that were produced by the original function. If we start with a
    single variable, x, and then multiply by 3 and add 2, then we would have a function of

    To undo the function, we would subtract 2 and divide by 3. Performing those operations would get us back to
    the original x-variable. So, the inverse of the function, denoted

    In this section, we will examine this process and learn how to verify and find inverse functions.

    UNIT V STUDY GUIDE

    More on Functions and Inequalities

    [https://online.columbiasouthern.edu/bbcswebdav/xid-146145209_1](https://online.columbiasouthern.edu/bbcswebdav/xid-146145209_1)

    [https://www.youtube.com/watch?v=DMrIagLiDNU](https://www.youtube.com/watch?v=DMrIagLiDNU)

    [https://www.youtube.com/watch?v=6ghkdsFbhMw](https://www.youtube.com/watch?v=6ghkdsFbhMw)

    MAT 1302, College Algebra 2

    UNIT x STUDY GUIDE

    Title

    The following videos can be viewed here as well as in your homework assignment. Please click the titles
    below to view the videos. A transcript and closed captioning are available once you access the videos.

    • Inverse Functions

    • Graphs of Inverse Functions

    Section 3.5: Rational Functions and Their Graphs

    Rational functions are functions that have a variable or expression in the denominator. All rational functions
    can be expressed as

    where p(x) and q(x) are polynomials and q(x) cannot equal zero. In this section, we will learn about the
    characteristics of rational functions and their graphs.

    The following videos can be viewed here as well as in your homework assignment. Please click the titles
    below to view the videos. A transcript and closed captioning are available once you access the videos.

    • Rational Functions, Part I

    • Rational Functions, Part II

    Section 3.6: Polynomial and Rational Inequalities

    As we have seen in previous units, inequalities use inequality signs that express solutions as greater than,
    less than, greater than or equal to, or less than or equal to. In this section, we will learn how to solve
    inequalities that contain polynomial and rational expressions.

    The following videos can be viewed here as well as in your homework assignment. Please click the titles
    below to view the videos. A transcript and closed captioning are available once you access the videos.

    • Polynomial Inequalities.

    • Rational Inequalities, Part I

    • Rational Inequalities, Part II

    Additional Help Available

    If you find yourself needing additional assistance with course material, please know that the Math Center is
    available and ready to help. Click the Math Center Request form to get connected with the Math Center’s
    tutors.

    Learning Activities (Nongraded)

    Nongraded Learning Activities are provided to aid students in their course of study. You do not have to submit
    them. If you have questions, contact your instructor for further guidance and information.

    Open your study plan in MyMathLab to see your progress and do supplemental practice exercises. The study
    plan will update each time you take an assessment. The study plan is for extra practice.

    For assistance with course content, you may contact your instructor or a math specialist. Click the Student
    Resources link to find contact information for the Math Center.

    [https://www.youtube.com/watch?v=kvSmESoYJHU](https://www.youtube.com/watch?v=kvSmESoYJHU)

    [https://www.youtube.com/watch?v=-n3L7Z0fWiA](https://www.youtube.com/watch?v=-n3L7Z0fWiA)

    [https://www.youtube.com/watch?v=iiqrdp96U0o](https://www.youtube.com/watch?v=iiqrdp96U0o)

    [https://www.youtube.com/watch?v=DfOU8DqsMh0](https://www.youtube.com/watch?v=DfOU8DqsMh0)

    [https://www.youtube.com/watch?v=f5j9BL8IvbI](https://www.youtube.com/watch?v=f5j9BL8IvbI)

    [https://www.youtube.com/watch?v=B7PVjgIZp30](https://www.youtube.com/watch?v=B7PVjgIZp30)

    [https://www.youtube.com/watch?v=_Ua9kyaC398](https://www.youtube.com/watch?v=_Ua9kyaC398)

    [https://mycsu.columbiasouthern.edu/student/forms/courses/math-center-request/](https://mycsu.columbiasouthern.edu/student/forms/courses/math-center-request/)

    **## UnitVDiscussionBoard.docx**

    Unit V Discussion Board

    Watch
    [_Video 3: The Power of "Yet,"_](https://mediaplayer.pearsoncmg.com/assets/mindset_3?centerwin=yes) and evaluate your course progress. Are you meeting your goals for the course? What goals do you have for the remainder of the class? What strategy can you implement to help you achieve those goals?

    Next, respond to another student's post. What are some ideas or tips that might help them reach their goals?

    Note: To locate the video transcript, please click on the settings and select English for the transcript to appear. You may also use closed-captioning.

    If no initial posts exist to allow for a response to be made, you may submit an additional initial post addressing another aspect of the unit topic.

    [https://mediaplayer.pearsoncmg.com/assets/mindset_3?centerwin=yes](https://mediaplayer.pearsoncmg.com/assets/mindset_3?centerwin=yes)

    Reply: Daniel Reid

    Hello everyone,

    As we started this course I had anxiety and for someone that has used explosives on the daily for over 25 years that is not something I usually have. At this point I have settled the nerves and realized my strengths and weaknesses. Fortunately I believe I am doing better than I thought I would. The words of Professor Morris during the live lecture about learning the rules really helped. If I am getting hung up its because I am not following the sequence correctly.

    Going forward I need to focus on the fine details. Much like in high school it was always the little details like negative signs or forgetting a parentheses that always got me a wrong answer and redoing each problem multiple times. Its still my mathematical downfall and I plan to work on it.

    I believe making the time to check work is a strategy that will help me pay attention to those fine details. However time consuming it does help with learning the sequences and rules that need to be applied to all equations.

    Reply: Michael Gish

    I am a very well-built procrastinator mostly by my own doing.  This is something added with anxiety and panic that causes confusion and pessimistic thoughts and processes. The best part of this is I am surprised everyday, by not the failures that occur, but by the things I actually succeed in. Writing this out is just the most anxious thing I have done all day and my day is just beginning.

    The only advice I can give is what I give myself. Small goals are a miracle that we can create.

    1. Open the computer.

    2. Open the class up.

    3. Open the assignment.

    4. Start the assignment

    5. Finish the assignment.

    These are all small goals that in the end create a big goal that you have finished. You may fail, but try again and in the end you will succeed if you want to.

    **## UnitV.pdf**

    MAT 1302, College Algebra 1

    Course Learning Outcomes for Unit V

    Upon completion of this unit, students should be able to:

    1. Solve algebraic functions.
    1.1 Apply the algebra of functions and the composition of functions to form new functions.
    1.2 Solve inverse functions algebraically and graphically.
    1.3 Find the inverse of a function.

    2. Apply algebraic principles to solve inequalities.

    2.1 Solve polynomial and rational inequalities.

    4. Graph unique functions.
    4.1 Graph inverse and rational functions.
    4.2 Identify vertical and horizontal asymptotes of rational functions.

    Required Unit Resources

    Chapter 2: Functions and Graphs, Sections 2.6, 2.7

    Chapter 3: Polynomial and Rational Functions, Sections 3.5, 3.6

    Unit Lesson

    This unit lesson provides an overview of concepts that you will learn in Unit V as well as links to required
    lesson videos. For additional instruction and examples, please refer to Sections 2.6, 2.7, 3.5, and 3.6 in your
    textbook. It is recommended to use the Unit V Homework Video Note-Taking Guide as you work through the
    videos.

    Section 2.6: Combinations of Functions; Composite Functions

    In this section, we will learn how to identify the variables that make a function work and combine functions to
    make new functions.

    The following videos can be viewed here as well as in your homework assignment. Please click the titles
    below to view the videos. A transcript and closed captioning are available once you access the videos.

    • Domains of Functions

    • Combining Functions
    Section 2.7: Inverse Functions

    The inverse of a function undoes the changes that were produced by the original function. If we start with a
    single variable, x, and then multiply by 3 and add 2, then we would have a function of

    To undo the function, we would subtract 2 and divide by 3. Performing those operations would get us back to
    the original x-variable. So, the inverse of the function, denoted

    In this section, we will examine this process and learn how to verify and find inverse functions.

    UNIT V STUDY GUIDE

    More on Functions and Inequalities

    [https://online.columbiasouthern.edu/bbcswebdav/xid-146145209_1](https://online.columbiasouthern.edu/bbcswebdav/xid-146145209_1)

    [https://www.youtube.com/watch?v=DMrIagLiDNU](https://www.youtube.com/watch?v=DMrIagLiDNU)

    [https://www.youtube.com/watch?v=6ghkdsFbhMw](https://www.youtube.com/watch?v=6ghkdsFbhMw)

    MAT 1302, College Algebra 2

    UNIT x STUDY GUIDE

    Title

    The following videos can be viewed here as well as in your homework assignment. Please click the titles
    below to view the videos. A transcript and closed captioning are available once you access the videos.

    • Inverse Functions

    • Graphs of Inverse Functions

    Section 3.5: Rational Functions and Their Graphs

    Rational functions are functions that have a variable or expression in the denominator. All rational functions
    can be expressed as

    where p(x) and q(x) are polynomials and q(x) cannot equal zero. In this section, we will learn about the
    characteristics of rational functions and their graphs.

    The following videos can be viewed here as well as in your homework assignment. Please click the titles
    below to view the videos. A transcript and closed captioning are available once you access the videos.

    • Rational Functions, Part I

    • Rational Functions, Part II

    Section 3.6: Polynomial and Rational Inequalities

    As we have seen in previous units, inequalities use inequality signs that express solutions as greater than,
    less than, greater than or equal to, or less than or equal to. In this section, we will learn how to solve
    inequalities that contain polynomial and rational expressions.

    The following videos can be viewed here as well as in your homework assignment. Please click the titles
    below to view the videos. A transcript and closed captioning are available once you access the videos.

    • Polynomial Inequalities.

    • Rational Inequalities, Part I

    • Rational Inequalities, Part II

    Additional Help Available

    If you find yourself needing additional assistance with course material, please know that the Math Center is
    available and ready to help. Click the Math Center Request form to get connected with the Math Center’s
    tutors.

    Learning Activities (Nongraded)

    Nongraded Learning Activities are provided to aid students in their course of study. You do not have to submit
    them. If you have questions, contact your instructor for further guidance and information.

    Open your study plan in MyMathLab to see your progress and do supplemental practice exercises. The study
    plan will update each time you take an assessment. The study plan is for extra practice.

    For assistance with course content, you may contact your instructor or a math specialist. Click the Student
    Resources link to find contact information for the Math Center.

    [https://www.youtube.com/watch?v=kvSmESoYJHU](https://www.youtube.com/watch?v=kvSmESoYJHU)

    [https://www.youtube.com/watch?v=-n3L7Z0fWiA](https://www.youtube.com/watch?v=-n3L7Z0fWiA)

    [https://www.youtube.com/watch?v=iiqrdp96U0o](https://www.youtube.com/watch?v=iiqrdp96U0o)

    [https://www.youtube.com/watch?v=DfOU8DqsMh0](https://www.youtube.com/watch?v=DfOU8DqsMh0)

    [https://www.youtube.com/watch?v=f5j9BL8IvbI](https://www.youtube.com/watch?v=f5j9BL8IvbI)

    [https://www.youtube.com/watch?v=B7PVjgIZp30](https://www.youtube.com/watch?v=B7PVjgIZp30)

    [https://www.youtube.com/watch?v=_Ua9kyaC398](https://www.youtube.com/watch?v=_Ua9kyaC398)

    [https://mycsu.columbiasouthern.edu/student/forms/courses/math-center-request/](https://mycsu.columbiasouthern.edu/student/forms/courses/math-center-request/)