Unit 4 Flashcard: Rational Functions Operations

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 expression?

Back

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

Front

What is the process for dividing rational functions?

Back

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

Front

What does it mean to subtract rational functions?

Back

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

Front

How do you find the least common denominator (LCD) of rational expressions?

Back

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

Front

What is the significance of factoring in rational functions?

Back

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

Front

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

Back

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

Front

What is a horizontal asymptote?

Back

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

Front

How do you determine the domain of a rational function?

Back

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

Front

Back

The result is -5.