Mary Jane Sterling - Algebra II - 1001 Practice Problems For Dummies (+ Free Online Practice)

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401 – 410 Sketch the graph of the polynomial.

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Chapter 8

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.

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

Determining the domain and range of the function

Removing discontinuities when possible

Finding limits at infinity and infinite limits

Writing equations of vertical, horizontal, and slant asymptotes

Solving for intercepts

Graphing rational functions

Don’t let common mistakes trip you up; watch out for the following ones when working with rational functions:

Categorizing a discontinuity as a vertical asymptote rather than removable

Not dividing correctly when solving for the horizontal asymptote

Sketching the curve on the wrong side of the horizontal asymptote

411–420 Determine the domain of the rational function.

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421–430 Find the removable discontinuity of the function.

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