Vertical asymptotes

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where a function approaches infinity or negative infinity as the input approaches a. It indicates values that make the function undefined.

Front

How do you find vertical asymptotes in a rational function?

Back

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

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Back

The vertical asymptote is x = 3.

Front

What happens to the graph of a function as it approaches a vertical asymptote?

Back

As the graph approaches a vertical asymptote, it tends to rise or fall without bound, moving towards positive or negative infinity.

Front

If a function has a vertical asymptote at x = -2, what does this imply about the function?

Back

It implies that the function is undefined at x = -2 and the values of the function will approach infinity or negative infinity as x approaches -2.

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Back

The vertical asymptotes are x = -2 and x = 4.

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Can a function have more than one vertical asymptote?

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Yes, a function can have multiple vertical asymptotes depending on the number of values that make the denominator zero.

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What is the significance of vertical asymptotes in graphing functions?

Back

Vertical asymptotes help identify where the function is undefined and indicate the behavior of the graph near those points.

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

Back

Vertical asymptotes indicate restrictions in the domain of a function, as they represent values that cannot be included.

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How do you determine if a function has a vertical asymptote at a specific x-value?

Back

Evaluate the limit of the function as x approaches that value. If the limit approaches infinity or negative infinity, there is a vertical asymptote.