4.1 Graphing 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 are the characteristics of rational functions?

Back

Rational functions can have vertical and horizontal asymptotes, holes, and can be discontinuous at certain points.

Front

What is a vertical asymptote?

Back

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

Front

How do you find vertical asymptotes?

Back

Vertical asymptotes are found by setting the denominator of the rational function equal to zero and solving for x.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line y = b that the function approaches as x approaches infinity or negative infinity.

Front

How do you find horizontal asymptotes?

Back

Horizontal asymptotes can be found by analyzing the degrees of the numerator and denominator polynomials.

Front

What is a hole in a rational function?

Back

A hole occurs at a value of x where both the numerator and denominator are zero, indicating a removable discontinuity.

Front

How do you find holes in a rational function?

Back

Holes are found by factoring the numerator and denominator and identifying common factors that cancel out.

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 value(s) that the function approaches but never reaches (asymptotes).