Rational Functions

Front

What are asymptotes?

Back

Asymptotes are lines that a graph approaches but never touches. They can be vertical, horizontal, or slant.

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

What is a horizontal asymptote?

Back

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

Front

How do you find vertical asymptotes?

Back

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

Front

How do you find horizontal asymptotes?

Back

Horizontal asymptotes are determined by comparing the degrees of the numerator and denominator of a rational function.

Front

What is the significance of the coefficients in horizontal asymptotes?

Back

The horizontal asymptote can be found by taking the ratio of the leading coefficients of the numerator and denominator if their degrees are the same.

Front

What is a slant asymptote?

Back

A slant (or oblique) asymptote occurs when the degree of the numerator is one greater than the degree of the denominator.

Front

What happens to the function at vertical asymptotes?

Back

At vertical asymptotes, the function tends to infinity or negative infinity, indicating a discontinuity.

Front

Can a function have more than one vertical asymptote?

Back

Yes, a rational function can have multiple vertical asymptotes depending on the factors of the denominator.

Front

What is the relationship between the degree of the numerator and denominator for horizontal asymptotes?

Back

If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0.