Rational Functions Review

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 an asymptote?

Back

An asymptote is a line that a graph approaches but never touches or crosses.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

Front

What is a vertical asymptote?

Back

A vertical asymptote is a vertical line that the graph of a function approaches as the function's value 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

What does it mean if a rational function has no horizontal asymptote?

Back

It means that as x approaches infinity or negative infinity, the function's value does not approach a finite number.

Front

When does a rational function have a horizontal asymptote at y=0?

Back

A rational function has a horizontal asymptote at y=0 when the degree of the numerator is less than the degree of the denominator.

Front

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

Back

If the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is at y = (leading coefficient of numerator)/(leading coefficient of denominator).

Front

What is a slant (oblique) asymptote?

Back

A slant asymptote occurs when the degree of the numerator is exactly one more than the degree of the denominator.

Front

How do you determine the horizontal asymptote when 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.