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Mathematics, Coding and Science Education

Helpful Tools for Calculus: Chapter 1

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Functions and Relations

This first chapter serves as an introduction to the types of functions and their uses. It can be treated as a speed run of Precalculus for the purpose of building a foundation for the calculus that begins in the next chapter. It is assumed that readers are already aware of these functions and their place in mathematics, so some content is introduced in chapters before they are explained on this website. The chapter begins with basic functions first introduced in Algebra I and developing important formulas to aid our understanding as we progress. Similar to the section numbers in Chapter 0, we will begin with the simplest building blocks and work our way to more complex types of functions. Algebra II functions are introduced in section 1.5 with Inverse Functions and continue through Logarithmic Functions. The most important part of Precalculus, Trigonometric Functions, is introduced in Section 1.9 and will develop an understanding of the unit circle, functions with angular inputs, relationships between functions and other formulas to help deepen our understanding. Finally, the last three sections of this chapter are dedicated to more complex functions and relations used more in much later sections of this book.


By the end of this chapter, you should understand:

  • The notation and meaning of each type of function
  • How to identify the domain and range of a relation
  • How to algebraically and graphically solve each type of function
  • The main characteristics of each function
  • Some applications for the different functions
  • How to use and create many of the formulas related to functions
  • The difference between a function and a relation
  • How to interpret graphs of relations

List of Topics in this Chapter:

  1. Functions and Graphing
  2. Linear Functions
  3. Quadratic Functions
  4. Polynomial and Rational Functions
  5. Inverse Functions
  6. Radical Functions
  7. Exponential Functions
  8. Logarithmic Functions
  9. Trigonometric Functions
  10. Inverse Trigonometric Functions
  11. Elementary and Composite Functions
  12. Hyperbolic Functions
  13. Implicit Equations
  14. Parametric Equations
  15. Polar Equations

Unit Daily Plan

Practice Problems

  1. Functions and Graphing
  2. Linear Functions
  3. Quadratic Functions
  4. Polynomial and Rational Functions
  5. Inverse Functions
  6. Radical Functions
  7. Exponential Functions
  8. Logarithmic Functions
  9. Trignometric Functions
  10. Inverse Trigonometric Functions
  11. Elementary and Composite Functions
  12. Hyperbolic Functions
  13. Implicit Equations
  14. Parametric Equations
  15. Polar Equations

Sample Assessments

  1. Functions and Graphing
  2. Linear Functions
  3. Quadratic Functions
  4. Polynomial and Rational Functions
  5. Inverse Functions
  6. Radical Functions
  7. Exponential Functions
  8. Logarithmic Functions
  9. Trignometric Functions
  10. Inverse Trigonometric Functions
  11. Elementary and Composite Functions
  12. Hyperbolic Functions
  13. Implicit Equations
  14. Parametric Equations
  15. Polar Equations

Solution Sets

  1. Functions and Graphing
  2. Linear Functions
  3. Quadratic Functions
  4. Polynomial and Rational Functions
  5. Inverse Functions
  6. Radical Functions
  7. Exponential Functions
  8. Logarithmic Functions
  9. Trignometric Functions
  10. Inverse Trigonometric Functions
  11. Elementary and Composite Functions
  12. Hyperbolic Functions
  13. Implicit Equations
  14. Parametric Equations
  15. Polar Equations

For the Next Sections, see Helpful Tools for Calculus, Chapter 2.