rational functions

Front

What is a rational function?

Back

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 imaginary line that your function never touches.

Front

What is the equation of a rational function?

Back

A mathematical expression that represents the relationship between the numerator and denominator of a rational function.

Front

What is a vertical asymptote?

Back

A vertical line that corresponds to the values of x that make the denominator of a rational function equal to zero.

Front

How do you find vertical asymptotes?

Back

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

Front

What is a horizontal asymptote?

Back

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

Front

How do you determine horizontal asymptotes for rational functions?

Back

Compare the degrees of the numerator and denominator polynomials.

Front

What is the end behavior of a rational function?

Back

The behavior of the function as x approaches positive or negative infinity.

Front

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

Back

The function either increases or decreases without bound as x approaches infinity.

Front

What is the significance of the numerator in a rational function?

Back

It determines the zeros of the function, where the function equals zero.