Rational Functions

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

How do you find the horizontal asymptote of a rational function?

Back

To find the horizontal asymptote, compare the degrees of the numerator and denominator polynomials.

Front

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

Back

The horizontal asymptote is y = 0.

Front

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

Back

The horizontal asymptote is y = the ratio of the leading coefficients.

Front

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

Back

There is no horizontal asymptote; the function may have a slant asymptote.

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 in a rational function?

Back

Vertical asymptotes occur at the values of x that make the denominator equal to zero, provided those values do not also make the numerator zero.

Front

What is the significance of the x-intercept in a rational function?

Back

The x-intercept is the point where the graph crosses the x-axis, found by setting the numerator equal to zero.