Rational Functions (Operations, Equations, Applications)

Front

Define 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 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

How do you multiply two rational functions?

Back

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

Front

What is an extraneous solution in rational equations?

Back

An extraneous solution is a solution that emerges from the algebraic process but does not satisfy the original equation.

Front

How do you find a common denominator for adding rational functions?

Back

To find a common denominator, identify the least common multiple (LCM) of the denominators of the rational functions.

Front

What is the process for solving a rational equation?

Back

To solve a rational equation, first find a common denominator, eliminate the denominators, solve the resulting equation, and check for extraneous solutions.

Front

What does it mean to simplify a rational expression?

Back

Simplifying a rational expression means reducing it to its lowest terms by canceling common factors in the numerator and denominator.

Front

How do you add two rational functions?

Back

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

Front

What is the standard form of a rational function?

Back

Front

What transformations occur when rewriting a rational function?

Back

Transformations can include shifts, stretches, or reflections of the graph of the function.