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Study Guides > College Algebra CoRequisite Course

Introduction to Rational Functions

Learning Outcomes

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, xx, produced. This is given by the equation C(x)=15,000x−0.1x2+1000C\left(x\right)=15,000x - 0.1{x}^{2}+1000. If we want to know the average cost for producing xx items, we would divide the cost function by the number of items, xx. The average cost function, which yields the average cost per item for xx items produced, is

f(x)=15,000x−0.1x2+1000xf\left(x\right)=\dfrac{15,000x - 0.1{x}^{2}+1000}{x}

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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