Rational Functions Test Review

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

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

Back

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

Front

What is the y-intercept of a function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, found by evaluating f(0).

Front

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

Back

To find the y-intercept, replace all x-values with 0 in the function.

Front

What are vertical asymptotes?

Back

Vertical asymptotes are lines x = a where the function approaches infinity or negative infinity, occurring when the denominator Q(x) equals zero.

Front

How do you find vertical asymptotes?

Back

Set the denominator Q(x) equal to zero and solve for x.

Front

What are horizontal asymptotes?

Back

Horizontal asymptotes are horizontal lines that the graph approaches as x approaches infinity or negative infinity.

Front

How do you determine the horizontal asymptote?

Back

Compare the degrees of the numerator and denominator: if the degree of the numerator is less, y = 0; if equal, y = a/b; if greater, none.

Front

What happens if the degree of the numerator is greater than the degree of the denominator?

Back

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

Front

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

Back

The degrees determine the behavior of the function at infinity and help identify horizontal asymptotes.