rational functions

Front

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.

Front

What is the general form of a rational function?

Back

Front

What is a vertical asymptote?

Back

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

Front

How do you find vertical asymptotes of a rational function?

Back

Set the denominator Q(x) = 0 and solve for x.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a line y = b that the function approaches as x approaches infinity or negative infinity.

Front

How do you find horizontal asymptotes of a rational function?

Back

1. If the degree of P < degree of Q, then y = 0. 2. If the degree of P = degree of Q, then y = leading coefficient of P / leading coefficient of Q. 3. If the degree of P > degree of Q, there is no horizontal asymptote.

Front

What is the significance of the leading coefficient in a rational function?

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The leading coefficient determines the end behavior of the function as x approaches infinity or negative infinity.

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What is the domain of a rational function?

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The domain is all real numbers except where the denominator Q(x) = 0.

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What is the range of a rational function?

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The range is the set of all possible output values, which can be determined by analyzing the function's behavior and asymptotes.

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What happens at the vertical asymptote?

Back

The function approaches infinity or negative infinity, indicating a discontinuity.