Rational Functions: Graphing Rational Functions and Domain and Range

Rational Functions

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Rational functions are defined as functions which can be written as the ratio of two polynomials. For example, the following are examples of rational functions:

x divided by the quantity of x minus 3
the quantity of x squared minus 3 x plus 1 divided by the quantity of x cubed plus 2 x squared minus 5 x minus 1


The denominator and the numerator are both made up of polynomials.

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The following are not rational functions:

absolute value of x divided by the quantity of x minus 3 natural log of x divided by the quantity of x minus 3


These are not rational functions because the numerators do not represent polynomials.