MA19.PRE.28

Mathematics (2019) Grade(s): 09-12 - Precalculus

MA19.PRE.28
Find inverse functions.

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

Aligned Learning Resources

Building Functions: Inverse Functions from Tables and Graphs

Design by Adaptive Theme