TEST Review Rationals

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 the function cannot take.

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What is the equation of a vertical asymptote?

Back

The equation of a vertical asymptote is typically found by setting the denominator of a rational function equal to zero and solving for x.

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How do you determine the number of vertical asymptotes in a function?

Back

Count the distinct values of x that make the denominator of the function equal to zero, as each corresponds to a vertical asymptote.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a line y = b where a function approaches the value b as x approaches infinity or negative infinity.

Front

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

Back

To find the horizontal asymptote, compare the degrees of the numerator and denominator. If the degree of the numerator is less, y = 0; if equal, y = leading coefficient of numerator/leading coefficient of denominator; if greater, there is no horizontal asymptote.

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What does it mean if a function has no horizontal asymptote?

Back

If a function has no horizontal asymptote, it means that as x approaches infinity or negative infinity, the function does not approach a specific value.

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What is the significance of vertical asymptotes in graphing functions?

Back

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

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Can a function have more than one vertical asymptote?

Back

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

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

Back

Vertical asymptotes correspond to values that are excluded from the domain of the function, as the function is undefined at those points.

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How do you graph a function with vertical and horizontal asymptotes?

Back

Start by plotting the asymptotes, then sketch the behavior of the function approaching these lines, ensuring to reflect the function's limits as x approaches the asymptotes.