Rational Functions

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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.

Tags

CCSS.HSF-IF.C.7D

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What is the general form of a rational function?

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The general form of a rational function is f(x) = P(x) / Q(x), where P(x) and Q(x) are polynomials.

Tags

CCSS.HSF-IF.C.7D

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What is an asymptote?

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

Tags

CCSS.HSF-IF.C.7D

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What is a vertical asymptote?

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A vertical asymptote occurs where the denominator of a rational function is zero, causing the function to be undefined.

Tags

CCSS.HSF-IF.C.7D

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How do you find vertical asymptotes?

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

Tags

CCSS.HSF-IF.C.7D

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What is a horizontal asymptote?

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A horizontal asymptote describes the behavior of a function as x approaches infinity or negative infinity.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find horizontal asymptotes for rational functions?

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For rational functions, compare the degrees of the numerator and denominator: If degree of numerator < degree of denominator, y=0; If equal, y = leading coefficient of numerator / leading coefficient of denominator; If greater, no horizontal asymptote.

Tags

CCSS.HSF-IF.C.7D

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What does it mean if a rational function has no horizontal asymptote?

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If a rational function has no horizontal asymptote, it means that as x approaches infinity or negative infinity, the function's value increases or decreases without bound.

Tags

CCSS.HSF-IF.C.7D

Front

What is the significance of holes in rational functions?

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A hole in a rational function occurs at a value of x that makes both the numerator and denominator zero, indicating a removable discontinuity.

Tags

CCSS.HSF-IF.C.7D

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How do you simplify a rational function?

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To simplify a rational function, factor both the numerator and denominator and cancel out any common factors.

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CCSS.HSA.APR.D.6