Rational Functions

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What is a rational function?

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What does it mean for a rational function to be undefined?

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A rational function is undefined at values of x that make the denominator equal to zero.

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The vertical asymptote is at x = 2.

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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 x approaches infinity or negative infinity.

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How do you find vertical asymptotes of a rational function?

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Vertical asymptotes can be found by setting the denominator equal to zero and solving for x.

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What is the significance of asymptotes in rational functions?

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Asymptotes indicate the behavior of the function as it approaches certain values, helping to understand the graph's shape.

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The horizontal asymptote is y = \frac{2}{4} = \frac{1}{2}.

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What happens to the graph of a rational function at its vertical asymptotes?

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The graph approaches the vertical asymptote but never touches or crosses it.

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The domain is all real numbers except x = 4.

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The range is all real numbers except y = 0.