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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:
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.
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