Big Ideas:
A function maps a set of inputs (a domain) to a set of outputs (a range), and each element of the domain is related to exactly one element of the range. An inverse of a function maps the outputs back to their corresponding inputs, and hence the range of a function is the domain of the inverse.
Because of this, only functions that are one-to-one (where each element of the range is uniquely associated with an element of domain) are invertible.
This lesson builds on the idea of a one-to-one function, which was introduced in Task 1: Determine if a function is one-to-one by examining the height and velocity of a projectile. In this task, students discover why a function must be one-to-one in order to be invertible by investigating a simple projectile motion model.
Vocabulary:
function, inverse, horizontal line test
Lesson plan