Vertical and Horizontal Asymptotes

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What is a vertical asymptote?

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A vertical asymptote is a line x = a where a function approaches infinity or negative infinity as x approaches a. It occurs when the function is undefined at x = a.

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How do you find vertical asymptotes algebraically?

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To find vertical asymptotes, set the denominator of a rational function equal to zero and solve for x.

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What is a horizontal asymptote?

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A horizontal asymptote is a line y = b that a function approaches as x approaches infinity or negative infinity.

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How do you determine horizontal asymptotes for rational functions?

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1. If the degree of the numerator is less than the degree of the denominator, y = 0 is the horizontal asymptote. 2. If the degrees are equal, y = leading coefficient of numerator / leading coefficient of denominator. 3. If the degree of the numerator is greater, there is no horizontal asymptote.

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What is the significance of asymptotes in graphing functions?

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Asymptotes help identify the behavior of a function as it approaches certain values, guiding the sketching of the graph.

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x = 3 and x = -4.

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What is the relationship between vertical asymptotes and the domain of a function?

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Vertical asymptotes indicate values that are excluded from the domain of a function, where the function is undefined.

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How can you identify horizontal asymptotes from a graph?

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Horizontal asymptotes can be identified by observing the value that the function approaches as x moves towards positive or negative infinity.