Graph the inverse of each one-to-one function.

Key Concepts

One-to-One Functions

A one-to-one function is a type of function where each output value corresponds to exactly one input value. This means that no two different inputs produce the same output, which is crucial for the existence of an inverse function. Graphically, a one-to-one function passes the horizontal line test, indicating that any horizontal line intersects the graph at most once.

Inverse Functions

An inverse function essentially reverses the effect of the original function. If a function f takes an input x and produces an output y, then its inverse f⁻¹ takes y back to x. The graph of an inverse function can be obtained by reflecting the graph of the original function across the line y = x, which visually demonstrates how the roles of inputs and outputs are switched.

Graphing Techniques

Graphing techniques involve methods used to accurately represent functions and their inverses on a coordinate plane. This includes identifying key points, understanding transformations, and applying reflections. For one-to-one functions, it is important to ensure that the graph is clear and that the inverse is correctly reflected across the line y = x, allowing for a visual comparison between the function and its inverse.