Horizontal Asymptotes in Rational Functions Flashcard

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What are horizontal asymptotes in rational functions?

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Horizontal asymptotes are lines that the graph of a rational function approaches as the input values (x) approach positive or negative infinity.

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How do you determine the horizontal asymptote of a rational function when the degree of the numerator is less than the degree of the denominator?

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

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There is no horizontal asymptote; the function will approach infinity or negative infinity.

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If the degrees of the numerator and denominator are the same, how is the horizontal asymptote found?

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By dividing the leading coefficients of the numerator and denominator.

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What is a 'hole' in a rational function?

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A hole occurs at a value of x where a factor in the numerator cancels with a factor in the denominator.

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What is the horizontal asymptote of a function if the degrees of the numerator and denominator are equal?

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The horizontal asymptote is the ratio of the leading coefficients.

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What does it mean if a rational function has no horizontal asymptote?

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It means that as x approaches infinity or negative infinity, the function's values do not approach a finite number.

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What is the significance of identifying horizontal asymptotes in rational functions?

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Identifying horizontal asymptotes helps in understanding the end behavior of the function.