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

How do you find the domain of a rational function?

Back

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

Front

What is a vertical asymptote?

Back

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

Front

How do you determine vertical asymptotes from a rational function?

Back

Vertical asymptotes can be found by setting the denominator equal to zero and solving for x.

Front

What is a horizontal asymptote?

Back

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

Front

How do you find horizontal asymptotes for rational functions?

Back

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

Front

What happens to a rational function at its vertical asymptotes?

Back

At vertical asymptotes, the function's value approaches infinity or negative infinity.

Front

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

Back

The numerator determines the function's zeros, which are the x-values where the function equals zero.

Front

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

Back

The denominator determines the function's vertical asymptotes and the domain restrictions.

Front

How do you simplify a rational function?

Back

To simplify a rational function, factor both the numerator and denominator and cancel out any common factors.