Graphing Rational Functions

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What is a Vertical Asymptote?

Back

A vertical asymptote is a line x = a where a rational function approaches infinity or negative infinity as the input approaches a. It indicates values that the function cannot take.

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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 function approaches as x approaches infinity or negative infinity. It indicates the behavior of the function at extreme values.

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How do you find the Vertical Asymptote of a rational function?

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To find the vertical asymptote, set the denominator of the rational function equal to zero and solve for x.

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How do you find the Horizontal Asymptote of a rational function?

Back

To find the horizontal asymptote, compare the degrees of the numerator and denominator. If the degree of the numerator is less, y = 0; if equal, y = leading coefficient of numerator/leading coefficient of denominator; if greater, there is no horizontal asymptote.

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What is the domain of a rational function?

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

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What are x-intercepts of a function?

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X-intercepts are points where the graph of the function crosses the x-axis, found by setting the numerator of the rational function equal to zero.

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What is the significance of the x-intercepts?

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X-intercepts indicate the values of x for which the function outputs zero, showing where the graph intersects the x-axis.

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What is the significance of the vertical asymptote?

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The vertical asymptote indicates values of x that the function cannot reach, often leading to infinite values.

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What is the significance of the horizontal asymptote?

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

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What happens to the graph of a rational function at the vertical asymptote?

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At the vertical asymptote, the graph will approach infinity or negative infinity, creating a break in the graph.