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Pre-AP Pre-Calculus Chapter 1, Section 5

This chapter focuses on inverse relations and functions, exploring how reversing the coordinates of ordered pairs leads to an inverse relation. It emphasizes the importance of the horizontal and vertical line tests in determining the nature of functions and their inverses. Students will learn how to identify which graphs represent functions and which have functional inverses. Additionally, it provides the definition of inverse functions, requirements for one-to-one functions, and algebraic examples. Homework assignments reinforce these concepts for deeper understanding.

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Pre-AP Pre-Calculus Chapter 1, Section 5

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  1. Pre-AP Pre-CalculusChapter 1, Section 5 Parametric Relations and Inverses 2013 - 2014

  2. Inverse Relations & Inverse Functions When you reverse the coordinates of all the ordered pair and solve for the dependent variable, you get an inverse relation. If a function fails the horizontal line test, the inverse function will fail the vertical line test meaning the inverse relation is not a function.

  3. Which of the 4 graphs are a function? Which ones have an inverse that is a function?

  4. Definition: Inverse Function • If f is a one-to-one function with domain D and range R, then the inverse function of f, denoted , is the function with domain R and range D defined by if and only if

  5. Find an equation for if

  6. Show algebraically that and are inverse functions.

  7. Show that has an inverse function and state any restrictions on the domains of f and .

  8. Homework • Ch. 1.5: Pg. 135-136: 9 – 21 odd, 27, 31, 33, 41 – 44,

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