Asymptotes and Discontinuities in Rational Functions

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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 the input values approach 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 input values approach a certain value, often where the function is undefined.

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What is a removable discontinuity?

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A removable discontinuity occurs at a point where a function is not defined, but can be made continuous by redefining the function at that point.

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What is the significance of vertical asymptotes in rational functions?

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Vertical asymptotes indicate values of the input where the function approaches infinity or negative infinity, often where the function is undefined.

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