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1001 Algebra II Practice Problems For Dummies by Mary Jane Sterling

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Chapter 8

Rational Functions

A rational function is special in that the function rule involves a fraction with a polynomial in both the numerator and the denominator. Rational functions have restrictions in their domain; any value creating a 0 in the denominator has to be excluded. Many of these exclusions are identified as vertical asymptotes. The x-intercepts of rational functions can be solved for by setting the numerator equal to 0; this is done after you’ve determined that there are no common factors in the numerator and denominator. A rational function can have a horizontal asymptote — as long as the highest power in the numerator is not greater than that in the denominator.

The Problems You’ll Work On

In this chapter, you’ll work with rational functions in the following ways:

check.png Determining the domain and range of the function

check.png Removing discontinuities, when possible

check.png Finding limits at infinity and infinite limits

check.png Writing equations of vertical, horizontal, and slant asymptotes

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