Unit 7: Rational Functions - Review 12/6/24

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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, typically in the form f(x) = P(x)/Q(x), where P and Q are polynomials.

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What does it mean to simplify a rational function?

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Simplifying a rational function involves factoring the numerator and denominator, canceling out common factors, and rewriting the function in its simplest form.

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How do you factor a polynomial?

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To factor a polynomial, you look for common factors, use techniques like grouping, or apply special formulas such as the difference of squares or the quadratic formula.

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What is the significance of canceling factors in rational functions?

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Canceling factors in rational functions helps to simplify the expression, making it easier to analyze, graph, or compute limits.

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What is the vertical asymptote of a rational function?

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A vertical asymptote occurs at values of x that make the denominator zero (Q(x) = 0) and are not canceled out by the numerator.

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What is the horizontal asymptote of a rational function?

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The horizontal asymptote describes the behavior of the function as x approaches infinity. It can be determined by comparing the degrees of the numerator and denominator.

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How do you find the x-intercepts of a rational function?

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To find the x-intercepts, set the numerator equal to zero (P(x) = 0) and solve for x.

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What is the domain of a rational function?

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The domain of a rational function includes all real numbers except those that make the denominator zero.

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What is the process for graphing a rational function?

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To graph a rational function, identify intercepts, asymptotes, and test points in intervals to determine the function's behavior.

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What is a hole in a rational function?

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A hole occurs at x-values that make both the numerator and denominator zero, indicating a removable discontinuity.