Characteristics of Rational Functions - Exit ticket

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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 the input 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 slant (oblique) asymptote?

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A slant asymptote occurs when the degree of the numerator is one greater than the degree of the denominator.

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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.

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What is the domain of a rational function?

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The domain of a rational function includes all real numbers except where the denominator is zero.

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How do you find the y-intercept of a rational function?

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The y-intercept is found by evaluating the function at x = 0, provided the function is defined at that point.

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What does it mean if a rational function has a hole?

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A hole occurs in a rational function when a factor in the numerator and denominator cancels out, indicating a point where the function is undefined.

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What is the significance of the horizontal asymptote?

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The horizontal asymptote indicates the behavior of a rational function as x approaches infinity or negative infinity.

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

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The horizontal asymptote can be determined by comparing the degrees of the numerator and denominator.