Characteristics of Rational Functions

Front

What is a rational function?

Back

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CCSS.HSF-IF.C.7D

Front

What are vertical asymptotes?

Back

Vertical asymptotes are lines that a graph approaches but never touches or crosses. They occur where the denominator of a rational function equals zero.

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CCSS.HSF-IF.C.7D

Front

What is a horizontal asymptote?

Back

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

Tags

CCSS.HSF-IF.C.7D

Front

How do you find vertical asymptotes of a rational function?

Back

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

Tags

CCSS.HSF-IF.C.7D

Front

What is the significance of horizontal asymptotes?

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Horizontal asymptotes indicate the behavior of a function as x approaches infinity or negative infinity, showing the value that the function approaches.

Tags

CCSS.HSF-IF.C.7D

Front

What is the x-intercept of a function?

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The x-intercept of a function is the point where the graph crosses the x-axis, found by setting the function equal to zero and solving for x.

Front

How do you determine the x-intercept of a rational function?

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To find the x-intercept, set the numerator of the rational function equal to zero and solve for x.

Tags

CCSS.HSF-IF.C.7D

Front

What is the relationship between the degree of the numerator and denominator in rational functions?

Back

The degree of the numerator and denominator determines the behavior of the function: if the degree of the numerator is less than the denominator, the horizontal asymptote is y=0; if they are equal, the asymptote is y=\frac{a}{b}, where a and b are the leading coefficients.

Tags

CCSS.HSF-IF.C.7D

Front

What is a hole in a rational function?

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A hole occurs in a rational function when a factor cancels out from both the numerator and denominator, indicating a point where the function is undefined.

Tags

CCSS.HSF-IF.C.7D

Front

What is the general form of a rational function?

Back

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CCSS.HSF-IF.C.7D