# Introduction to Rational Functions

### LEARNING OBJECTIVES

By the end of this lesson, you will be able to:- Use arrow notation.
- Solve applied problems involving rational functions.
- Find the domains of rational functions.
- Identify vertical asymptotes.
- Identify horizontal asymptotes.
- Graph rational functions.

Suppose we know that the cost of making a product is dependent on the number of items, *x*, produced. This is given by the equation [latex]C\left(x\right)=15,000x - 0.1{x}^{2}+1000\\[/latex]. If we want to know the average cost for producing *x* items, we would divide the cost function by the number of items, *x*.

The average cost function, which yields the average cost per item for *x* items produced, is

Many other application problems require finding an average value in a similar way, giving us variables in the denominator. Written without a variable in the denominator, this function will contain a negative integer power.

In the last few sections, we have worked with polynomial functions, which are functions with non-negative integers for exponents. In this section, we explore rational functions, which have variables in the denominator.

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- Precalculus.
**Provided by:**OpenStax**Authored by:**Jay Abramson, et al..**Located at:**https://openstax.org/books/precalculus/pages/1-introduction-to-functions.**License:**CC BY: Attribution.**License terms:**Download For Free at : http://cnx.org/contents/[email protected]..