Rational Function (Asymptotes)

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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.

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What is the domain of a rational function?

Back

The domain of a rational function consists of all real numbers except where the denominator equals zero.

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What is the range of a rational function?

Back

The range of a rational function includes all real numbers except for any horizontal asymptotes.

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What is a vertical asymptote?

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A vertical asymptote is a vertical line x = a where the function approaches infinity or negative infinity as x approaches a.

Front

How do you find vertical asymptotes?

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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 horizontal line y = b that the function approaches as x approaches infinity or negative infinity.

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How do you find horizontal asymptotes?

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Horizontal asymptotes can be found by analyzing the degrees of the numerator and denominator polynomials.

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What happens to a rational function at its vertical asymptotes?

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At vertical asymptotes, the function's value approaches infinity or negative infinity.

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What is the significance of the horizontal asymptote?

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The horizontal asymptote indicates the value that the function approaches as x becomes very large or very small.

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What is the difference between vertical and horizontal asymptotes?

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Vertical asymptotes are related to the values of x that make the denominator zero, while horizontal asymptotes describe the behavior of the function as x approaches infinity.