# Precalculus: Data, Functions, and Graphs

Educator Edition

Contributor | University of Michigan |

Course | MATH 105, Data, Functions, and Graphs. Presents concepts from four points of view: geometric (graphs), numeric (tables), symbolic (formulas), and written (verbal descriptions). The emphasis is on the mathematical modeling of real-life problems using linear, polynomial, exponential, logarithmic, and trigonometric functions. |

Textbook | Functions Modeling Change: A Preparation for Calculus, Connally, Hughes-Hallett, Gleason, et. al. 5th Edition, or a textbook of your choice. |

## Customize your Student Experience

Edfinity is a full-featured homework system. Use this problem series as-is, or mix-and-match with other series or your own problems as desired. Edfinity gives you complete control over the every aspect of students' online assessment experience.

## Goals

Math 105 serves both as a preparatory class to the calculus sequences and as a class for students who are interested in strengthening their math skills.

## Powered by WeBWorK

This problem series includes WeBWorK-enhanced problems. WeBWorK problems are highly sophisticated, supporting the representation and manipulation of mathematical objects such as vectors, points, matrices, intervals, and complex numbers, with customizable answer checkers. Students are encouraged to make multiple attempts until they succeed, and given immediate feedback on correctness.

Edfinity provides full access to the WeBWorK Open Public Library (OPL), a collection of over 20,000 rich, interactive problems across a wide range of math and science subjects, including college algebra, discrete mathematics, probability and statistics, single and multivariable calculus, differential equations, linear algebra and complex analysis.

## Problem Sets

- 1.1 Functions and Function Notation
- 1.2 Rules of Change
- 1.3-1.4 Linear Functions
- 1.5 Modeling with Linear Functions
- 2.1 Input and Output
- 2.2 Domain and Range
- 2.3 Piecewise-defined Functions
- 2.4 Preview of Transformations: Shift
- 2.5 Preview of Converse and Inverse Functions
- 2.6 Concavity
- 3.1 Introduction to the Family of Quadratic Equations
- 3.2 The Vertex of a Parabola
- 4.1 Introduction to the Family of Exponential Functions
- 4.2 Comparing Exponential and Linear Functions
- 4.3 Graphs of Exponential Functions
- 4.5 The Number e
- 5.1 Logarithms and their Properties
- 5.2 Logarithms and Exponential Models
- 5.3 The Logarithmic Function and its Applications
- 6.1 Shifts, Reflections, and Symmetry
- 6.2 Vertical Stretches and Compressions
- 6.3 Horizontal Stretches and Combinations of Transformations
- 7.1 Introduction to Periodic Functions
- 7.2 The Sine and Cosine Functions
- 7.3 Radians and Arc Length
- 7.5 Sinusoidal Functions
- 7.8 & 9.1: Inverse Trigonometric Functions
- 8.1 Trig. Functions and Right Angles
- 10.1 Composition of Functions
- 10.2 Invertability and Properties of Inverse Functions
- 10.3 Combinations of Functions
- 11.1 Power Functions and Proportionality
- 11.2-11.3 Polynomial Functions and the Short-run Behavior of Polynomials
- 11.3 The Short-run Behavior of Polynomials
- 11.4-11.5 Rational Functions and the Short-run Behavior of Rational Functions
- 11.6 Comparing Power, Exponential, and Log Functions

## License

This is a multi-student, educator license. You will be able to manage an online course with your students, and monitor their progress.