Rational Function Transformations

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

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.

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

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

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

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

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