Unpacked Content
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.
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
