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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.
TextbookFunctions 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.

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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

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