Rational Funtions - Slant Asymptotes

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What is a rational function?

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A rational function is a function that can be expressed as the quotient of two polynomials, i.e., f(x) = P(x)/Q(x), where P and Q are polynomials.

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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 vertical, horizontal, or slant (oblique).

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What is a slant asymptote?

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A slant asymptote occurs when the degree of the numerator is exactly one more than the degree of the denominator in a rational function.

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How do you find the slant asymptote of a rational function?

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To find the slant asymptote, perform polynomial long division on the rational function. The quotient (ignoring the remainder) gives the equation of the slant asymptote.

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y = x.

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y = x - 7.

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y = 2x + 24.

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y = 4x + 23.

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y = x - 5.

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What happens to the value of a rational function as x approaches infinity?

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As x approaches infinity, the value of the rational function approaches the value of its slant asymptote.