Find Asymptotes of 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 are the types of asymptotes?

Back

There are three types of asymptotes: vertical, horizontal, and oblique (slant).

Front

How do you find vertical asymptotes?

Back

Vertical asymptotes occur where the denominator of a rational function is zero and the numerator is not zero.

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 determine the horizontal asymptote of a rational function?

Back

1. If the degree of the numerator is less than the degree of the denominator, y=0. 2. If the degrees are equal, y = leading coefficient of numerator / leading coefficient of denominator. 3. If the degree of the numerator is greater, there is no horizontal asymptote.

Front

What is a hole in a graph?

Back

A hole occurs in a graph when a factor in the numerator and denominator cancels out, indicating that the function is undefined at that point.

Front

How do you find the x-intercepts of a rational function?

Back

To find the x-intercepts, set the numerator equal to zero and solve for x.

Front

How do you find the y-intercept of a rational function?

Back

To find the y-intercept, evaluate the function at x=0.

Front

What is the significance of the leading coefficients in horizontal asymptotes?

Back

The leading coefficients determine the value of the horizontal asymptote when the degrees of the numerator and denominator are equal.