Key Features of Rational Functions

Front

What is a rational function?

Back

A rational function is a function that can be expressed as the ratio of two polynomials, typically in the form f(x) = P(x)/Q(x), where P and Q are polynomials.

Front

What is a vertical asymptote?

Back

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

Front

How do you find vertical asymptotes?

Back

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

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

How do you find holes in a rational function?

Back

To find holes, factor both the numerator and denominator, and identify common factors that can be canceled.

Front

What is an x-intercept?

Back

An x-intercept is the point where the graph of a function crosses the x-axis, found by setting the y-value to zero.

Front

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

Back

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

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 horizontal asymptotes for rational functions?

Back

Horizontal asymptotes can be determined by comparing the degrees of the numerator and denominator polynomials.

Front

What happens if 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.