Horizontal Asymptotes in Rational Functions Flashcard

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What is a vertical asymptote?

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A vertical asymptote is a line x = a where a rational function approaches infinity or negative infinity as the input approaches a. It occurs when the denominator of the function equals zero and the numerator does not equal zero at that point.

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How do you find vertical asymptotes in a rational function?

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To find vertical asymptotes, set the denominator of the rational function equal to zero and solve for x. The values of x that make the denominator zero are the vertical asymptotes.

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What is a hole in a rational function?

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A hole occurs in a rational function when a factor in the numerator cancels with a factor in the denominator. This means the function is undefined at that point, but the limit exists.

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What is a horizontal asymptote?

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A horizontal asymptote is a horizontal line y = b that the graph of a function approaches as x approaches infinity or negative infinity. It indicates the behavior of the function at extreme values.

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How do you determine the horizontal asymptote of a rational function?

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To determine the horizontal asymptote, compare the degrees of the numerator and denominator: 1. If the degree of the numerator is less than the degree of the denominator, y = 0. 2. If they 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 variable do we use to identify vertical asymptotes?

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We use the variable x to identify vertical asymptotes.

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What happens to the function at a vertical asymptote?

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At a vertical asymptote, the function approaches infinity or negative infinity, indicating that the function is undefined at that point.

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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 does not approach a specific value.