QZZ 2.6/2.7 Asymptotes

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What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as the input (x) approaches positive or negative infinity.

Tags

CCSS.HSF-IF.C.7D

Front

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

Back

Tags

CCSS.HSF-IF.C.7D

Front

What is a vertical asymptote?

Back

A vertical asymptote is a vertical line that the graph of a function approaches as the input (x) approaches a certain value, typically where the function is undefined.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find vertical asymptotes in a rational function?

Back

Vertical asymptotes occur at values of x that make the denominator of a rational function equal to zero, provided that the numerator is not also zero at those points.

Tags

CCSS.HSF-IF.C.7D

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What is a hole in a graph?

Back

A hole in a graph occurs at a point where both the numerator and denominator of a rational function are zero, indicating that the function is undefined at that point.

Tags

CCSS.HSF-IF.C.7D

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How do you identify the location of a hole in a rational function?

Back

To find the location of a hole, factor both the numerator and denominator of the rational function and identify the common factors. The x-value that makes the common factor zero is the location of the hole.

Tags

CCSS.HSF-IF.C.7D

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What is the significance of asymptotes in graphing functions?

Back

Asymptotes help to understand the behavior of a function as it approaches certain values, guiding the sketching of the graph and indicating limits of the function.

Tags

CCSS.HSF-IF.C.7D

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Back

The vertical asymptote is x=2, and there is a horizontal asymptote at y=0.

Tags

CCSS.HSF-IF.C.7D

Front

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

Back

As the graph approaches a horizontal asymptote, the y-values of the function get closer to the value of the asymptote but never actually reach it.

Tags

CCSS.HSF-IF.C.7D

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Can a function have more than one vertical asymptote?

Back

Yes, a function can have multiple vertical asymptotes, typically occurring at different values of x where the denominator is zero.

Tags

CCSS.HSF-IF.C.7D