Classify the function as a polynomial function, rational function, or root function, and then find the domain. Write the domain in interval notation.
-$$g ( x ) = \frac { 2 x } { x ^ { 2 } - 9 }$$
A) rational function; $( \infty , \infty )$
B) rational function; $( 9 , \infty )$
C) rational function; $( - \infty , 0 ) \cup ( 0 , \infty )$
D) rational function; $( \infty , - 3 ) \cup ( - 3,3 ) \cup ( 3 , \infty )$

Question

Quizplus · Accepted Answer

The function is a rational function because it is the ratio of two polynomials. The domain excludes values that make the denominator zero, which are $x = 3$ and $x = -3$. Thus, the domain is $(-\infty, -3) \cup (-3, 3) \cup (3, \infty)$.

Classify the Function as a Polynomial Function, Rational Function, or Root