Operations with 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 simplify a rational function?

Back

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

Front

What is 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 does it mean to perform operations with rational functions?

Back

Performing operations with rational functions involves addition, subtraction, multiplication, or division of two or more rational functions.

Front

How do you add two rational functions?

Back

To add two rational functions, find a common denominator, rewrite each function with that denominator, and then combine the numerators.

Front

What is the process for subtracting rational functions?

Back

Subtracting rational functions follows the same process as addition: find a common denominator, rewrite, and then combine the numerators.

Front

How do you multiply rational functions?

Back

To multiply rational functions, multiply the numerators together and the denominators together, then simplify if possible.

Front

What is the method for dividing rational functions?

Back

To divide rational functions, multiply by the reciprocal of the divisor and then simplify.

Front

What is a vertical asymptote in the context of rational functions?

Back

A vertical asymptote occurs at values of x that make the denominator zero, indicating where the function approaches infinity.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote describes the behavior of a rational function as x approaches infinity or negative infinity.