Rational Functions Review

Front

What are asymptotes?

Back

Asymptotes are lines that a graph approaches but never touches. They can be vertical (VA) or horizontal (HA).

Front

What is the vertical asymptote of a rational function?

Back

The vertical asymptote is found by setting the denominator of the rational function equal to zero and solving for x.

Front

What is the horizontal asymptote of a rational function?

Back

The horizontal asymptote is determined by comparing the degrees of the numerator and denominator of the rational function.

Front

How do you find the x-intercepts of a rational function?

Back

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

Front

What does it mean if a rational function has no horizontal asymptote?

Back

If a rational function has no horizontal asymptote, it means that as x approaches infinity or negative infinity, the function does not approach a specific y-value.

Front

What is the significance of the degrees of the numerator and denominator?

Back

The degrees of the numerator and denominator help determine the behavior of the rational function, including the existence and location of horizontal asymptotes.

Front

What is the formula for finding the horizontal asymptote when the degrees are equal?

Back

If the degrees of the numerator and denominator are equal, the horizontal asymptote is found by dividing the leading coefficients.

Front

What is the formula for finding the horizontal asymptote when the degree of the numerator is less than the degree of the denominator?

Back

If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0.

Front

What is the formula for finding the horizontal asymptote when the degree of the numerator is greater than the degree of the denominator?

Back

If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.

Front

What is a rational function?

Back

A rational function is a function that can be expressed as the ratio of two polynomials.