UP:MA19.PRE.28

Vocabulary

  • Inverse
  • Domain/output of a relation/function
  • Range/output of a relation/function
  • Horizontal line test (one-to-one)
  • Inverse Function
  • Composition
  • Invertible Function
  • Non-Invertible Function
  • Restricting the Domain

Knowledge

Students know:
  • The domain and range of a given relation or function.
  • Algebraic properties.
  • Symmetry about the line y = x.
  • Techniques for composing functions.
  • The composition of a function and its inverse is the identity function.
  • When (x,y) is a point on an invertible function, (y,x) is a point on the inverse.
  • In order for a function to have an inverse function, the original function must have a one-to-one correspondence.

Skills

Students are able to:
  • Find the inverse of function.
  • Accurately perform algebraic properties to find the inverse.
  • Accurately identify restrictions on a non-invertible function that allow it to be invertible.
  • Accurately find the composition of two functions.

Understanding

Students understand that:
  • The graphical and algebraic relationship between a function and its inverse.
  • The process of finding the inverse of a function.
  • The inverse of a function interchanges the input and output values from the original function.
  • The inverse of a function must also be a function to exist and the domain may need to be restricted to make this occur.
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