Rational Functions

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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 general form of a rational function?

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What is an asymptote?

Back

An asymptote is a line that a graph approaches but never touches or crosses.

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What is a horizontal asymptote?

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A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches infinity or negative infinity.

Front

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

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1. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. 2. If the degrees are equal, the horizontal asymptote is y = \frac{a}{b}, where a and b are the leading coefficients. 3. If the degree of the numerator is greater, there is no horizontal asymptote.

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What is a vertical asymptote?

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A vertical asymptote is a vertical line that the graph of a function approaches as the input approaches a certain value, typically where the denominator is zero.

Front

How do you find vertical asymptotes of a rational function?

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To find vertical asymptotes, set the denominator equal to zero and solve for x.

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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 function equal to zero.

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What are y-intercepts of a function?

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Y-intercepts are points where the graph of the function crosses the y-axis, found by evaluating the function at x = 0.

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y = 2.