Key Features of Rational Functions

Front

What is a rational function?

Back

Front

What is the domain of a rational function?

Back

The domain of a rational function is all real numbers except where the denominator is zero.

Front

What is an excluded point in a rational function?

Back

An excluded point is a value of x that makes the denominator zero, resulting in a discontinuity in the function.

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

What are vertical asymptotes?

Back

Vertical asymptotes are lines x = a where the function approaches infinity or negative infinity as x approaches a.

Front

How do you find vertical asymptotes?

Back

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

Front

What are horizontal asymptotes?

Back

Horizontal asymptotes are lines y = b that the function approaches as x approaches infinity or negative infinity.

Front

How do you determine horizontal asymptotes?

Back

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

Front

What is the horizontal asymptote 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 is the horizontal asymptote if the degrees of the numerator and denominator are equal?

Back

If the degrees are equal, the horizontal asymptote is y = \frac{a}{b} where a and b are the leading coefficients of the numerator and denominator.