Front

What is a rational function?

Back

A rational function is a function that can be expressed as the quotient of two polynomials, i.e., \( f(x) = \frac{P(x)}{Q(x)} \) where \( P(x) \) and \( Q(x) \) are polynomials.

Tags

CCSS.HSF-IF.C.7D

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.

Tags

CCSS.HSA.APR.D.6

Front

What is the domain of a rational function?

Back

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

Front

What does it mean to perform operations on rational functions?

Back

Performing operations on rational functions includes addition, subtraction, multiplication, and division of two or more rational functions.

Tags

CCSS.HSA.APR.D.6

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.

Tags

CCSS.HSA.APR.D.7

Front

What is the process for subtracting rational functions?

Back

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

Tags

CCSS.HSA.APR.D.7

Front

How do you multiply two rational functions?

Back

To multiply two rational functions, multiply the numerators together and the denominators together: \( \frac{P(x)}{Q(x)} \cdot \frac{R(x)}{S(x)} = \frac{P(x)R(x)}{Q(x)S(x)} \).

Tags

CCSS.HSA.APR.D.7

Front

What is the method for dividing rational functions?

Back

To divide rational functions, multiply by the reciprocal of the divisor: \( \frac{P(x)}{Q(x)} \div \frac{R(x)}{S(x)} = \frac{P(x)}{Q(x)} \cdot \frac{S(x)}{R(x)} \).

Tags

CCSS.HSA.APR.D.6

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 that the function approaches infinity.

Tags

CCSS.HSF-IF.C.7D

Front

What is a horizontal asymptote?

Back

A horizontal asymptote describes the behavior of a rational function as \( x \) approaches infinity. It can be found by comparing the degrees of the numerator and denominator.

Tags

CCSS.HSF-IF.C.7D