Rational Functions Review

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

What are extraneous solutions?

Back

Extraneous solutions are solutions that emerge from the process of solving an equation but do not satisfy the original equation.

Front

How do you check for extraneous solutions?

Back

To check for extraneous solutions, substitute the solution back into the original equation to see if it holds true.

Front

What is the process for multiplying rational expressions?

Back

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

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 subtract rational expressions with the same denominator?

Back

To subtract rational expressions with the same denominator, subtract the numerators and keep the common denominator.

Front

What is the formula for subtracting rational expressions with different denominators?

Back

To subtract rational expressions with different denominators, find a common denominator, rewrite each expression, and then subtract the numerators.

Front

What is the significance of factoring in rational functions?

Back

Factoring helps to simplify rational expressions and to identify restrictions on the variable (where the denominator cannot be zero).

Front

What is the domain of a rational function?

Back

The domain of a rational function consists of all real numbers except those that make the denominator zero.

Front

How do you find the vertical asymptotes of a rational function?

Back

Vertical asymptotes occur at the values of x that make the denominator zero, provided these values do not also make the numerator zero.