OL Attributes of 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, typically in the form f(x) = P(x)/Q(x), where P and Q are polynomials.

Front

What is an x-intercept?

Back

An x-intercept is the point where a function crosses the x-axis, which occurs when f(x) = 0.

Front

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

Back

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

Front

What is a vertical asymptote?

Back

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

Front

How do you find vertical asymptotes in a rational function?

Back

Vertical asymptotes occur at values of x that make the denominator zero, provided the numerator is not also zero at those points.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line y = b that the graph of a 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 the degree of the numerator is less, y = 0; if equal, y = leading coefficient of numerator/leading coefficient of denominator; if greater, no horizontal asymptote.

Front

What is a hole in the graph of a rational function?

Back

A hole occurs at a point where both the numerator and denominator are zero, indicating that the function is undefined at that point.

Front

How do you find the x-value of a hole in a rational function?

Back

To find the x-value of a hole, factor the numerator and denominator, and set the common factors equal to zero.

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 function at infinity and the existence of horizontal asymptotes.