# Precalculus: Data, Functions, and Graphs

used at University of Michigan

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.

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## 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.

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. 1.1 Functions and Function Notation
2. 1.2 Rules of Change
3. 1.3-1.4 Linear Functions
4. 1.5 Modeling with Linear Functions
5. 2.1 Input and Output
6. 2.2 Domain and Range
7. 2.3 Piecewise-defined Functions
8. 2.4 Preview of Transformations: Shift
9. 2.5 Preview of Converse and Inverse Functions
10. 2.6 Concavity
11. 3.1 Introduction to the Family of Quadratic Equations
12. 3.2 The Vertex of a Parabola
13. 4.1 Introduction to the Family of Exponential Functions
14. 4.2 Comparing Exponential and Linear Functions
15. 4.3 Graphs of Exponential Functions
16. 4.5 The Number e
17. 5.1 Logarithms and their Properties
18. 5.2 Logarithms and Exponential Models
19. 5.3 The Logarithmic Function and its Applications
20. 6.1 Shifts, Reflections, and Symmetry
21. 6.2 Vertical Stretches and Compressions
22. 6.3 Horizontal Stretches and Combinations of Transformations
23. 7.1 Introduction to Periodic Functions
24. 7.2 The Sine and Cosine Functions
25. 7.3 Radians and Arc Length
26. 7.5 Sinusoidal Functions
27. 7.8 & 9.1: Inverse Trigonometric Functions
28. 8.1 Trig. Functions and Right Angles
29. 10.1 Composition of Functions
30. 10.2 Invertability and Properties of Inverse Functions
31. 10.3 Combinations of Functions
32. 11.1 Power Functions and Proportionality
33. 11.2-11.3 Polynomial Functions and the Short-run Behavior of Polynomials
34. 11.3 The Short-run Behavior of Polynomials
35. 11.4-11.5 Rational Functions and the Short-run Behavior of Rational Functions
36. 11.6 Comparing Power, Exponential, and Log Functions