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What is a vertical asymptote?

Back

A vertical asymptote is a line that a graph approaches but never touches or crosses. It occurs where the function is undefined, typically where the denominator of a rational function equals zero.

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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 the variable.

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What is the significance of vertical asymptotes in graphing functions?

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Vertical asymptotes indicate values where the function approaches infinity or negative infinity, helping to understand the behavior of the graph near those points.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as the input values approach positive or negative infinity.

Front

How do you determine horizontal asymptotes for rational functions?

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To find horizontal asymptotes, compare the degrees of the numerator and denominator. If the degree of the numerator is less, the asymptote is y=0. If they are equal, the asymptote is y= the ratio of the leading coefficients.

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What is the end behavior of a function?

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End behavior describes how the values of a function behave as the input approaches positive or negative infinity, often determined by horizontal asymptotes.

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

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Vertical asymptotes are determined by the values that make the denominator of a rational function equal to zero.

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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 is defined for all real numbers and does not approach infinity at any point.

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What is the difference between vertical and horizontal asymptotes?

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Vertical asymptotes are vertical lines where the function approaches infinity, while horizontal asymptotes are horizontal lines that the function approaches as the input goes to infinity.

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How can you identify the presence of an asymptote in a graph?

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Asymptotes can be identified in a graph by observing where the graph approaches a line but does not touch or cross it.