Graphing Rational Functions

Front

What is a rational function?

Back

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What does it mean to shift a graph left or right?

Back

Front

What does it mean to shift a graph up or down?

Back

Front

How do you find the domain of a rational function?

Back

Front

What is a vertical asymptote?

Back

Front

What is a horizontal asymptote?

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Front

How do you determine the 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. The solutions are the x-values of the vertical asymptotes.

Front

How do you determine the horizontal asymptotes of a rational function?

Back

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 equal, y = leading coefficient of numerator/leading coefficient of denominator; if greater, there is no horizontal asymptote.

Front

What is the range of a rational function?

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The range of a rational function is the set of all possible output values (y-values). It can often be determined by analyzing the function's behavior and any horizontal asymptotes.

Front

What is the significance of the leading coefficient in a rational function?

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The leading coefficient of the numerator and denominator affects the end behavior of the function and helps determine horizontal asymptotes.