Operations with 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, i.e., \( f(x) = \frac{P(x)}{Q(x)} \) where \( P(x) \) and \( Q(x) \) are polynomials.

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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 the denominator and then cancel any common factors.

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CCSS.HSA.APR.D.6

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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 is zero.

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What does it mean to perform operations on rational functions?

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Performing operations on rational functions includes addition, subtraction, multiplication, and division of two or more rational functions.

Tags

CCSS.HSA.APR.D.6

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How do you add two rational functions?

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To add two rational functions, find a common denominator, rewrite each function with that denominator, and then combine the numerators.

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CCSS.HSA.APR.D.7

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What is the process for subtracting rational functions?

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Subtracting rational functions involves finding a common denominator, rewriting each function, and then subtracting the numerators.

Tags

CCSS.HSA.APR.D.7

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How do you multiply two rational functions?

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To multiply two rational functions, multiply the numerators together and the denominators together: \( \frac{P(x)}{Q(x)} \cdot \frac{R(x)}{S(x)} = \frac{P(x)R(x)}{Q(x)S(x)} \).

Tags

CCSS.HSA.APR.D.7

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What is the method for dividing rational functions?

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To divide rational functions, multiply by the reciprocal of the divisor: \( \frac{P(x)}{Q(x)} \div \frac{R(x)}{S(x)} = \frac{P(x)}{Q(x)} \cdot \frac{S(x)}{R(x)} \).

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CCSS.HSA.APR.D.6

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What is a vertical asymptote in the context of rational functions?

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A vertical asymptote occurs at values of \( x \) that make the denominator zero, indicating that the function approaches infinity.

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 rational function as \( x \) approaches infinity. It can be found by comparing the degrees of the numerator and denominator.

Tags

CCSS.HSF-IF.C.7D