Functions

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Table of Contents

Research Questions

Upon completion of this section you will be competent enough to answer the following:

  • What is a relation?
  • What is a function?
  • Are all relations functions?
  • Are all functions relations?
  • What is meant by the domain?
  • What is meant by the range?
  • What do we use the vertical line test for?
  • What is an injective (one-to-one) function?
  • What is the algebraic method of determining if a function is injective?
  • What is the horizontal line test used for?
  • What is a surjective function?
  • What is a bijective function?
  • How do we find the inverse of a function?
  • What is the geometric relationship of the inverse function to the original function?
  • Can we find the inverse of a function which is not bijective?
  • What is meant by the composition of two functions?
  • Show that $ff^{-1}(x)=x$ and $f^{-1}f(x)=x$
  • What transformations can we apply to functions?

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