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Study Guides > College Algebra

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

[latex]f\left(x\right)=\frac{15,000x - 0.1{x}^{2}+1000}{x}[/latex]

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]..
  • College Algebra. Provided by: OpenStax Authored by: Abramson, Jay et al.. License: CC BY: Attribution. License terms: Download for free at http://cnx.org/contents/[email protected].