Rational Functions

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What is a rational function?

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What are asymptotes in the context of rational functions?

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Asymptotes are lines that the graph of a function approaches but never touches. They can be vertical, horizontal, or oblique.

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How do you find vertical asymptotes of a rational function?

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Vertical asymptotes occur where the denominator of the rational function is equal to zero, provided the numerator is not also zero at that point.

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What is the equation of a vertical asymptote?

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How do you find horizontal asymptotes of a rational function?

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Front

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 is the range of a rational function?

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The range of a rational function is all real numbers except for the values that the function approaches but never reaches, often determined by horizontal asymptotes.

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How do you translate the graph of a rational function?

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To translate the graph of a rational function, you adjust the function's equation by adding or subtracting values from the x or y variables.

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What is the significance of the horizontal asymptote in a rational function?

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The horizontal asymptote indicates the behavior of the function as x approaches infinity or negative infinity.

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What does it mean if a rational function has no vertical asymptotes?

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If a rational function has no vertical asymptotes, it means that the denominator does not equal zero for any real number, indicating that the function is defined for all real numbers.