Unit 4 Review of Rational Funtions

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 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

What is a horizontal asymptote?

Back

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

Front

How do you find vertical asymptotes?

Back

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

Front

What does it mean 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.

Front

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

Back

If the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is y = the ratio of the leading coefficients.

Front

What does it mean if 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 hole in a rational function?

Back

A hole occurs in a rational function at a value of x that makes both the numerator and denominator equal to zero, indicating a removable discontinuity.

Front

How do you simplify a rational function?

Back

To simplify a rational function, factor both the numerator and denominator and cancel any common factors.

Front

What is the process to multiply two rational functions?

Back

To multiply two rational functions, multiply the numerators together and the denominators together, then simplify if possible.