Vertical asymptotes

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What is a vertical asymptote?

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A vertical asymptote is a vertical line that a graph approaches but never touches or crosses. It occurs where a function's value becomes infinite.

Tags

CCSS.HSF-IF.C.7D

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How do you find vertical asymptotes in a rational function?

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To find vertical asymptotes, set the denominator of the rational function equal to zero and solve for x.

Tags

CCSS.HSF-IF.C.7D

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

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If a function has no vertical asymptotes, it means that the function does not approach infinity for any value of x in its domain.

Tags

CCSS.HSF-IF.C.7D

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If a function has vertical asymptotes at x = 2 and x = -3, what does this indicate?

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This indicates that as x approaches 2 or -3, the function's value approaches infinity or negative infinity.

Tags

CCSS.HSF-IF.C.7D

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What is the relationship between vertical asymptotes and the domain of a function?

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Vertical asymptotes indicate values that are excluded from the domain of the function, as the function is undefined at these points.

Tags

CCSS.HSF-IF.C.7D

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How many vertical asymptotes can a rational function have?

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A rational function can have one or more vertical asymptotes, depending on the degree of the polynomial in the denominator.

Tags

CCSS.HSF-IF.C.7D

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The vertical asymptote is at x = 3.

Tags

CCSS.HSF-IF.C.7D

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Back

The vertical asymptotes are at x = -2 and x = 5.

Tags

CCSS.HSF-IF.C.7D

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What happens to the graph of a function at a vertical asymptote?

Back

The graph of the function will approach the vertical asymptote but will never touch or cross it.

Tags

CCSS.HSF-IF.C.7D

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Can vertical asymptotes occur in functions other than rational functions?

Back

Yes, vertical asymptotes can also occur in some logarithmic and trigonometric functions.

Tags

CCSS.HSF-IF.C.7D