Vertical and Horizontal Asymptotes (ALG 2)

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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 the input approaches a. It occurs when the denominator of a rational function equals zero.

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How do you find vertical asymptotes?

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To find vertical asymptotes, set the denominator of the 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 find horizontal asymptotes for rational functions?

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1. Compare the degrees of the numerator and denominator. 2. If the degree of the numerator is less, y = 0. 3. If they are equal, y = leading coefficient of numerator / leading coefficient of denominator. 4. If the degree of the numerator is greater, there is no horizontal asymptote.

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y = rac{3}{2}

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There is no horizontal asymptote.

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Vertical asymptotes: x = 2 and x = -2; Horizontal asymptote: y = 0.

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What does it mean if a function has no vertical asymptotes?

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It means that the function does not approach infinity or negative infinity for any finite value of x.

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What is the significance of the degree of a polynomial in finding asymptotes?

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The degree of the polynomial helps determine the behavior of the function as x approaches infinity, which is crucial for identifying horizontal asymptotes.

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x = 3