4.5 Rational Functions

  • For a rational function, find the domain and graph the function, identifying all of the asymptotes.

  • Solve applied problems involving rational functions.

Now we turn our attention to functions that represent the quotient of two polynomials. Whereas the sum, the difference, or the product of two polynomials is a polynomial, in general the quotient of two polynomials is not itself a polynomial.

A rational number can be expressed as the quotient of two integers, p/q, where q0. A rational function is formed by the quotient of two polynomials, p(x)/q(x), where q(x)0. Here are some examples of rational functions and their graphs.

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