4.1 Graphing Rational Functions

Front

What is a rational function?

Back

A rational function is a function that can be expressed as the quotient of two polynomials, where the denominator is not zero.

Front

What is the general form of a rational function?

Back

The general form is f(x) = P(x)/Q(x), where P(x) and Q(x) are polynomials.

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where the function approaches infinity or negative infinity as x approaches a.

Front

How do you find vertical asymptotes of a rational function?

Back

Set the denominator Q(x) = 0 and solve for x.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a line y = b that the function approaches as x approaches infinity or negative infinity.

Front

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

Back

Compare the degrees of the numerator and denominator: If degree of numerator < degree of denominator, y = 0; if equal, y = leading coefficient of numerator/leading coefficient of denominator; if greater, no horizontal asymptote.

Front

What is a hole in a rational function?

Back

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

Front

How do you find holes in a rational function?

Back

Factor both the numerator and denominator, and identify common factors that can be canceled.

Front

What does it mean if the degree of the numerator is less than the degree of the denominator?

Back

The horizontal asymptote is y = 0.

Front

What does it mean if the degree of the numerator is equal to the degree of the denominator?

Back

The horizontal asymptote is determined by the ratio of the leading coefficients.