### Learning Outcomes

By the end of this section, you will be able to:

- Solve a rational formula for a specified variable
- Solve an application using a formula that must be solved for a specified variable
- Solve applications by defining and solving rational equations.
- Solve an application using a formula containing a radical expression
- Graph radical functions using tables and transformations
- Solve an application by writing and solving a proportion

You’ve studied how to identify and manipulate rational expressions and radical expressions such as

[latex]\dfrac{5}{x+2}, \quad \text{ or } \quad \dfrac{x}{x^2-9}, \quad \text{ and } \quad \sqrt{2x+1}[/latex].

You’ve also seen how to solve rational and radical equations (equations in which the variable is contained within one or more rational or radical expressions). This module will extend those concepts to the language of functions, where you’ll learn about graphing and applying rational and radical functions to real-world situations.

To prepare, it will be important to practice applications of rational and radical equations and see how radical functions are graphed using a few key points. This module includes a problem-solving technique known as variation, which involves writing relationships as proportions in order to solve for an unknown, so it will be helpful to review proportions as well.

Warm up for this module by refreshing important concepts and skills you’ll need for success. As you study these review topics, recall that you can also return to Algebra Essentials any time you need to refresh the basics.

### Recall for success

Look for red boxes like this one throughout the text. They’ll show up just in time to give helpful reminders of the math you’ll need, right where you’ll need it.