**Assignment 5.1: Manipulating Functions**

Complete the following problems. Be sure to show all work.

- Use the graph of to sketch the graph of the following functions. Also, describe in words each transformation that you applied.
- Use the graph of to sketch the graph of the following functions. Also, describe in words each transformation that you applied.
- Find the domain of the following functions. Give your answer in interval notation.
- Given and find , , , and .
- Given and find , , and .
- Find the inverse of the following one-to-one functions.
- Use composition to verify that the following functions are inverses.
- Sketch the graphs of the following functions and their inverses.

Simplify your answers.

Simplify your answers.