Rational Graphs

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

How do you determine the Horizontal Asymptote?

Back

Compare the degrees of the numerator and denominator.

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where the function approaches infinity or negative infinity as x approaches a.

Front

How do you find a vertical asymptote?

Back

Set the denominator of the rational function equal to zero and solve for x.

Front

What are holes in a rational function?

Back

Holes occur at values of x where a factor in the numerator cancels with a factor in the denominator.

Front

How do you find the holes of a rational function?

Back

Identify the common factors in the numerator and denominator and set them equal to zero.

Front

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

Back

The degrees help determine the horizontal asymptote and the end behavior of the rational function.

Front

What happens when the degree of the numerator is less than the degree of the denominator?

Back

The horizontal asymptote is y = 0.

Front

What happens when the degree of the numerator is equal to the degree of the denominator?

Back

The horizontal asymptote is y = leading coefficient of numerator / leading coefficient of denominator.

Front

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

Back

There is no horizontal asymptote; the function may have an oblique asymptote.