Slant Asymptotes

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What is a slant asymptote?

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A slant asymptote (or oblique asymptote) is a line that a function approaches as the input (x) approaches infinity or negative infinity, typically occurring when the degree of the numerator is one higher than the degree of the denominator in a rational function.

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How do you find the slant asymptote of a rational function?

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What is the significance of slant asymptotes in graphing rational functions?

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Slant asymptotes help in understanding the end behavior of rational functions, indicating how the function behaves as x approaches infinity or negative infinity.

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What is the difference between horizontal and slant asymptotes?

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Horizontal asymptotes occur when the degrees of the numerator and denominator are equal or the degree of the numerator is less than that of the denominator, while slant asymptotes occur when the degree of the numerator is exactly one more than that of the denominator.

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If a rational function has a degree of 3 in the numerator and 2 in the denominator, what type of asymptote can be expected?

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The function will have a slant asymptote.

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How can you determine if a function has a slant asymptote?

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Check the degrees of the numerator and denominator. If the degree of the numerator is one more than the degree of the denominator, the function has a slant asymptote.