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, where the denominator is not zero.

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 the denominator and then cancel any common factors.

Tags

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 equals zero.

Front

What does it mean to perform operations with rational functions?

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Performing operations with rational functions involves addition, subtraction, multiplication, or division of two or more rational functions.

Tags

CCSS.HSA.APR.D.6

Front

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.

Tags

CCSS.HSA.APR.D.7

Front

What is the process for subtracting rational functions?

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Subtracting rational functions follows the same process as addition: find a common denominator, rewrite, and then combine the numerators.

Tags

CCSS.HSA.APR.D.7

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How do you multiply rational functions?

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To multiply rational functions, multiply the numerators together and the denominators together, then simplify if possible.

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 and then simplify.

Tags

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 where the function approaches infinity.

Tags

CCSS.HSF-IF.C.7D

Front

What is a horizontal asymptote?

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

Tags

CCSS.HSF-IF.C.7D