rational functions

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What is a rational function?

Back

A rational function is a function that can be expressed as the quotient of two polynomials, where the denominator is not zero.

Front

What is the general form of a rational function?

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Front

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 x approaches a.

Front

How do you find vertical asymptotes of a rational function?

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Vertical asymptotes are found by setting the denominator equal to zero and solving for x.

Front

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.

Front

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

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To find the horizontal asymptote, compare the degrees of the numerator and denominator polynomials.

Front

What happens if the degree of the numerator is less than the degree of the denominator?

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If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0.

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What happens if the degree of the numerator is equal to the degree of the denominator?

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If the degrees are equal, the horizontal asymptote is y = \frac{a}{b}, where a and b are the leading coefficients of the numerator and denominator.

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What happens if the degree of the numerator is greater than the degree of the denominator?

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If the degree of the numerator is greater, there is no horizontal asymptote; the function may have an oblique asymptote.

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What is an oblique asymptote?

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An oblique asymptote occurs when the degree of the numerator is exactly one more than the degree of the denominator.