Rational Function Transformations

Front

What is a rational function?

Back

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 the set of all possible output values, which can vary based on the function's behavior and asymptotes.

Front

What is a vertical asymptote?

Back

Front

How do you find vertical asymptotes?

Back

Vertical asymptotes can be found by setting the denominator of the rational function equal to zero and solving for x.

Front

What is a horizontal asymptote?

Back

Front

How do you find horizontal asymptotes?

Back

Horizontal asymptotes can be found by analyzing the degrees of the numerator and denominator polynomials.

Front

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

Back

The degree of the numerator and denominator determines the behavior of the function at infinity and the existence of horizontal asymptotes.

Front

What is a hole in a rational function?

Back

A hole occurs in a rational function at a value of x where both the numerator and denominator are zero, indicating a removable discontinuity.

Front

What is the effect of transformations on rational functions?

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Transformations such as shifts, stretches, and reflections can change the position and shape of the graph of a rational function.