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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What is a 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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How do you find the horizontal asymptote of a rational function?

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What is a 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 vertical asymptotes?

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Vertical asymptotes occur at values of x that make the denominator of a rational function equal to zero, provided the numerator is not also zero at those points.

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What is the significance of horizontal asymptotes in graphing?

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Horizontal asymptotes indicate the end behavior of a function as x approaches infinity or negative infinity.

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What does it mean if a function has no horizontal asymptote?

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If a function has no horizontal asymptote, it means that as x approaches infinity or negative infinity, the function's value continues to increase or decrease without bound.