Unit 4 Flashcard: Rational Functions Operations

A rational function is a function that can be expressed as the quotient of two polynomials, where the denominator is not zero.

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

To divide rational functions, multiply the first function by the reciprocal of the second function and then simplify.

Subtracting rational functions involves finding a common denominator, rewriting each function, and then subtracting the numerators.

The least common denominator is found by determining the least common multiple of the denominators of the rational expressions.

Factoring helps to simplify rational functions and identify any restrictions on the variable that may arise from the denominator.

A vertical asymptote occurs where the denominator of a rational function equals zero, indicating that the function approaches infinity.

A horizontal asymptote describes the behavior of a rational function as the variable approaches infinity, indicating the value the function approaches.

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

The result is -5.