Basic Rational Functions & Asymptotes

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 are Asymptotes?

Back

Asymptotes are lines that a graph approaches but never touches. They can be vertical, horizontal, or oblique.

Front

How do you find vertical asymptotes?

Back

Vertical asymptotes occur where the denominator of a rational function is zero, provided the numerator is not also zero at that point.

Front

How do you find horizontal asymptotes?

Back

Horizontal asymptotes are found by comparing the degrees of the numerator and denominator polynomials.

Front

What is the domain of a rational function?

Back

The domain of a rational function includes all real numbers except where the denominator is zero.

Front

What is the range of a rational function?

Back

The range of a rational function includes all real numbers except for the values that make the function undefined.

Front

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

Back

The degree of the numerator and denominator helps determine the behavior of the function as x approaches infinity or negative infinity.

Front

What is a hole in a rational function?

Back

A hole occurs in a rational function at a point where both the numerator and denominator are zero, indicating a removable discontinuity.

Front

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

Back

The x-intercepts are found by setting the numerator equal to zero and solving for x.

Front

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

Back

The y-intercept is found by evaluating the function at x=0, provided the function is defined at that point.