Characteristics of Rational Functions

Front

What is a rational function?

Back

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.

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.

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.

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.

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?

Back

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

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.

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.

Front

What is the general form of a rational function?

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