Which graphs in Exercises 96–99 represent functions that have inverse functions?

Key Concepts

Function Definition

A function is a relation that assigns exactly one output for each input from its domain. This means that for every x-value, there is a unique y-value. Understanding the definition of a function is crucial for determining whether a graph represents a function and whether it can have an inverse.

Horizontal Line Test

The horizontal line test is a method used to determine if a function has an inverse that is also a function. If any horizontal line intersects the graph of the function more than once, the function does not have an inverse that is a function. This test is essential for analyzing the graphs in the given exercises.

Inverse Functions

An inverse function essentially reverses the effect of the original function. If a function f takes an input x to an output y, then its inverse f⁻¹ takes y back to x. For a function to have an inverse, it must be one-to-one, meaning it passes the horizontal line test, ensuring that each output corresponds to a unique input.