MyLab Math for Reasoning with Functions I -- Student Access Kit

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.

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

Overview

Arithmetic with Fractions

Combining Like Terms

Coordinate Plane

Dimensional Analysis

Distributive Property

Exponent Rules

Factoring

Factoring Polynomials

Four Representations of Functions

Graphing Technology

Interval Notation

Lines

Order of Operations

Roots and Radicals

Scientific Notation

Slope

Solving Quadratic Equations

Writing Principles