Asymptotes

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What is an asymptote?

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An asymptote is a line that a graph approaches but never touches. It can be horizontal, vertical, or oblique.

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Define horizontal asymptote.

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A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

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Define vertical asymptote.

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A vertical asymptote is a vertical line that the graph of a function approaches as the function's value approaches infinity or negative infinity.

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How do you find horizontal asymptotes for rational functions?

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To find horizontal asymptotes of a rational function, compare the degrees of the numerator and denominator. If the degree of the numerator is less, the asymptote is y=0. If they are equal, the asymptote is y=ratio of leading coefficients.

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How do you find vertical asymptotes for rational functions?

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Vertical asymptotes occur where the denominator of a rational function is zero and the numerator is not zero.

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The vertical asymptote is x = 3.

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The function has 2 vertical asymptotes at x = 3 and x = -3.

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What happens to the graph of a function at a vertical asymptote?

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At a vertical asymptote, the graph of the function approaches infinity or negative infinity.