MyMathLab for Reasoning with Functions I -- Student Access Kit

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  • Edition: 1st
  • Format: Nonspecific Binding
  • Copyright: 8/25/2016
  • Publisher: Pearson

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This course is a credit-bearing course in Precalculus Math

MyMathLab for Reasoning with Functions I  is part of a series of MyMathLab courses built to support the New Mathways Project developed by the Charles A. Dana Center. The New Mathways Project embodies the Dana Center’s vision for a systemic approach to improving student success and completion through implementation of processes, strategies, and structures built around three mathematics pathways.

Reasoning with Functions I  is the first of two college-level courses designed to prepare students to enter calculus and succeed in STEM coursework that requires a thorough knowledge of functions and algebraic reasoning. Students build a strong foundation in functions and their behavior by using multiple representations and explicit covariational reasoning to investigate and explore quantities, their relationships, and how these relationships change. It is designed as a five-contact-hour course, with the Intermediate and College Algebra skills needed to prepare for Reasoning with Functions II.  The MyMathLab course designed for use with Reasoning with Functions I provides:

  • Interactive content to help prepare students for active classroom time
  • In-Class Interactive Lessons to support students through an active classroom experience, accompanied by notebook PDFs
  • Homework assignments designed to assess conceptual understanding of important skills and concepts
  • Additional resources for instructors to help facilitate an interactive and engaging classroom


Built in MyMathLab

Content developed by the Charles A. Dana Center at The University of Texas at Austin will be delivered through MyMathLab. MyMathLab is an online homework, tutorial, and assessment program that engages students and improves results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts. 

Author Biography

MyMathLab for Reasoning with Functions I was developed by the Charles A. Dana Center at The University of Texas–Austin. The Dana Center brings together experienced faculty from two- and four-year institutions to author, review, field-test, and revise the New Mathways Project curricular materials.


The Dana Center develops and scales effective math and science innovations to support educators, administrators, and policy makers in creating seamless transitions throughout the K14 system for all students. Their work, based on research and two decades of experience, focuses on K–16 mathematics and science education with an emphasis on strategies for improving student engagement, motivation, persistence, and achievement. They develop innovative curricula, tools, protocols, and instructional supports and deliver powerful instructional and leadership development.

Table of Contents

Lesson 1: Describing Quantities and Their Relationships

1.A — Talking About Quantities

1.B — Our Learning Community

1.C — Talking About Quantities (Continued)

1.D — Functions

1.E — Functions (Continued)


Lesson 2: Working with Inputs and Outputs

2.A — Independence and Dependence

2.B — Processes

2.C — Domain and Range

2.D — More with Function Notation


Lesson 3: Exploring Linear, Exponential, and Periodic Models

3.A — Linear Population Growth

3.B — Models of Exponential Growth and Decay

3.C — Models With Periodic Functions

3.D — Comparing Linear, Exponential, and Periodic Functions

3.E — Forming Effective Study Groups


Lesson 4: Exploring Logarithmic Models

4.A — Introduction to Piecewise Defined Functions

4.B — Interpreting the Behavior of Logarithmic Functions

4.C — Interpreting the Behavior of Logarithmic Functions (Continued)

4.D — Investigating Other Functions


Lesson 5: Modeling Constant Change

5.A — Linear Functions and Equations

5.B — Linear Functions and Equations (Continued)

5.C — Straight Talk About Lines

5.D — Straight Talk About Lines (Continued)


Lesson 6: Making Predictions with Lines

6.A — Slope and Intercept

6.B — Golfing on the Moon

6.C — Finding Intersections of Lines

6.D — Graphing With Technology


Lesson 7: Modeling with Two Lines

7.A — Solving Systems of Linear Equations Graphically

7.B — Determining the Number of Solutions

7.C — Solving Systems Using Substitution

7.D — Elimination by Addition

7.E — Maximum Heart Rate


 Lesson 8: Using Matrices to Find Solutions

8.A — Matrices and Linear Systems

8.B — Row Echelon Form

8.C — Strategies for Solving Linear Systems


Lesson 9: Modeling with Curves

9.A — Quadratic Functions

9.B — Properties of Quadratic Functions

9.C — Unit Cost


Lesson 10: Shifting, Scaling, and Inverting Quadratic Functions

10.A — Transformations of Quadratic Functions

10.B — Composing and Inverting Transformations

10.C — Modeling With Quadratic Functions

10.D — Solving Quadratic Equations

10.E — Rates of Change and Total Change


Lesson 11: Exploring Inverse Relationships

11.A — Reversing a Quadratic Function

11.B — The Inverse of a Linear Function

11.C — The Inverse of a Quadratic Function

11.D — What Is a Meter?

11.E — How Fast?


Lesson 12: Modeling with Power Functions

12.A — Introduction to Power Functions

12.B — Introduction to Power Functions (Continued)

12.C — Illuminance


Lesson 13: Working with Volume and Optimization Models

13.A — Graphing Polynomial Functions

13.B — Building Polynomial Models

13.C — Optimization

13.D — Strategies for Factoring Polynomials


Lesson 14: Interpreting Change in Polynomial Models

14.A — Average Rates of Change

14.B — Average Rates of Change (Continued)

14.C — Modeling with Polynomial Functions

14.D — Modeling with Polynomial Functions (Continued)


Lesson 15: Working with Fractional Exponents

15.A — Fractional Exponents

15.B — Functions With Fractional Exponents

15.C — Graphs of Functions With Fractional Exponents


Lesson 16: Understanding Discontinuities and End Behavior

16.A — Discontinuities of Rational Functions

16.B — End Behavior of Rational Functions


Lesson 17: Exploring Asymptotic Behavior

17.A — Vertical Asymptotes

17.B — Behavior Near Vertical Asymptotes

17.C — Vertical Asymptotes vs. Holes

17.D — Strategies for Understanding Vertical Asymptotes


Lesson 18: Modeling with Rational Functions

18.A — You’re Getting Very Sleepy…

18.B — Reducing Pollution

18.C — Food Costs


Lesson 19: Exploring Graphs of Rational Functions

19.A — Graphing Rational Functions

19.B — Extreme Values of Rational Functions

19.C — Drug Concentration

19.D — Special Relativity


Lesson 20: Understanding Addition and Composition of Rational Functions

20.A — Composition of Rational Functions

20.B — Adding It All Up

20.C — Adding Rational Functions

20.D — Adding Rational Functions (Continued)


Lesson 21: Comparing Graphs of Functions

21.A — Exponential Functions — Revisited

21.B — Other Forms of Exponential Functions

21.C — Comparing Exponential and Linear Functions


Lesson 22: Interpreting Change in Exponential Models

22.A — Half-life and Decay Models

22.B — Doubling Time and Growth Models

22.C — Comparing Exponential Functions


Lesson 23: Exploring Other Exponential Models

23.A — Newton’s Law of Cooling

23.B — Drug Accumulation and Exponential Models

23.C — Surge Functions


Lesson 24: Analyzing Linear Approximations of Exponential Models

24.A — Linear Approximations of Exponential Functions

24.B — Compound Interest


Lesson 25: Exploring Logistic Growth and Oscillation

25.A — The Logistic Function

25.B — Decaying Oscillations

25.C — Decaying Oscillations (Continued)

25.D — Charging and Discharging Capacitors


Lesson 26: Inverting Exponential Functions

26.A — Inverse Exponentials

26.B — Logarithms

26.C — Graphing Logs

26.D — Log Laws

26.E — Logarithmic Scales


Lesson 27: Solving Exponential and Logarithmic Equations

27.A — Savings Bonds

27.B — How Do You Rank?

27.C — Earthquake!

27.D — Extraneous Solutions




Student Resources


Arithmetic with Fractions

Combining Like Terms

Coordinate Plane

Dimensional Analysis

Distributive Property

Exponent Rules


Factoring Polynomials

Four Representations of Functions

Graphing Technology

Interval Notation


Order of Operations

Roots and Radicals

Scientific Notation


Solving Quadratic Equations

Writing Principles


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