Final Review Unit 6 Rational Functions

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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 the input (x) approaches positive or negative infinity. For rational functions, it can often be determined by comparing the degrees of the numerator and denominator.

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How do you determine 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 = (leading coefficient of numerator)/(leading coefficient of denominator). 3. If the degree of the numerator is greater, there is no horizontal asymptote.

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What are excluded values in rational functions?

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Excluded values are values of x that make the denominator of a rational function equal to zero. These values are not in the domain of the function.

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How do you find excluded values in a rational expression?

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To find excluded values, set the denominator equal to zero and solve for x. The solutions are the excluded values.

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What is the first step in multiplying rational expressions?

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The first step is to factor all numerators and denominators completely before multiplying.

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How do you divide rational expressions?

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To divide rational expressions, multiply by the reciprocal of the second expression. That is, change the division to multiplication and flip the second fraction.

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What is the process for simplifying a rational expression?

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

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What is the significance of the leading coefficient in rational functions?

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The leading coefficient affects the end behavior of the function and helps determine the horizontal asymptote when the degrees of the numerator and denominator are equal.

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What does it mean for a rational function to have no horizontal asymptote?

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A rational function has no horizontal asymptote if the degree of the numerator is greater than the degree of the denominator.

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