Graphing Rational Functions Practice

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.

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

Back

To find the horizontal asymptote of a rational function, compare the degrees of the numerator and denominator. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. If they are equal, the asymptote is y = (leading coefficient of numerator)/(leading coefficient of denominator). If the degree of the numerator is greater, there is no horizontal asymptote.

Front

What is the domain of a rational function?

Back

The domain of a rational function is all real numbers except where the denominator is zero.

Front

What is the range of a rational function?

Back

The range of a rational function is all real numbers except for the value of the horizontal asymptote.

Front

What are vertical asymptotes?

Back

Vertical asymptotes are vertical lines that the graph of a function approaches as x approaches a certain value, typically where the denominator of a rational function is zero.

Front

How do you find vertical asymptotes?

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

Front

What is the significance of asymptotes in graphing rational functions?

Back

Asymptotes help to determine the behavior of the graph of a rational function, indicating where the graph will not cross or touch certain lines.

Front

What is the difference between a hole and a vertical asymptote?

Back

A hole occurs when a factor in the numerator and denominator cancels out, indicating a point where the function is undefined. A vertical asymptote occurs where the function approaches infinity.

Front

How do you determine the intercepts of a rational function?

Back

To find the x-intercepts, set the numerator equal to zero and solve for x. To find the y-intercept, evaluate the function at x = 0.

Front

What is the end behavior of a rational function?

Back

The end behavior of a rational function describes how the function behaves as x approaches positive or negative infinity, often determined by the horizontal asymptote.