rational functions

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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, where the denominator is not zero.

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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 x approaches a.

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How do you find vertical asymptotes of a rational function?

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

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What is a horizontal asymptote?

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A horizontal asymptote is a line y = b that the graph of a rational 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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Horizontal asymptotes can be determined by comparing the degrees of the numerator and denominator polynomials.

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What happens to the graph of a rational function as x approaches a vertical asymptote?

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As x approaches a vertical asymptote, the function's value increases or decreases without bound (approaches infinity or negative infinity).

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The graph approaches y = 5 as x gets larger.

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Back

The graph approaches y = 0 as x gets larger.

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What does it mean if a rational function is undefined at a certain x-value?

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It means that the function's denominator equals zero at that x-value, leading to division by zero.

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What is the significance of the degrees of the numerator and denominator in rational functions?

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The degrees determine the horizontal asymptote and the end behavior of the function.