This lesson on vertical and horizontal asymptotes of rational functions teaches students how to identify vertical asymptotes by setting the denominator equal to zero and solving for x. The lesson also explains how to determine the degrees of the polynomial expressions in the numerator and denominator to locate horizontal asymptotes. If the degrees are equal, the horizontal asymptote is a line crossing the y-axis at a ratio of the leading coefficients. The lesson concludes with a graph illustrating how to plot vertical and horizontal asymptotes and zeros.
Locating the vertical and horizontal asymptotes of a rational function. A reminder to set the denominator to zero to locate the vertical asymptotes and to compare the degrees of the expressions in the numerator and denominator to determine if there are horizontal asymptotes and if there are; what they are.
Questions answered by this video:
What are asymptotes of rational functions?
How do you locate the vertical and horizontal asymptotes of rational functions?
What are the vertical asymptotes of f(x) = (3x^2 - 27)/(x^2 - 36)?
What does it mean for a function to have an asymptote?
What is the difference between a vertical and horizontal asymptote?
If the degree of the numerator and the degree of the denominator of a rational function are equal, how do you find the horizontal asymptote for the rational function?
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This lesson explains the concept of an asymptote and shows an example of how to find both vertical and horizontal asymptotes for a rational function. All steps and methods are shown and explained clearly.