Classify the function as a polynomial function, rational function, or root function, and then find the domain. Write the domain in interval notation.
-$$h ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 8 }$$
A) rational function; $( \infty , \infty )$
B) rational function; $( - 8 , \infty )$
C) rational function; $( - \infty , 0 ) \cup ( 0 , \infty )$
D) rational function; $( - \infty , - 8 ) \cup ( - 8 , \infty )$

Question

Quizplus · Accepted Answer

The function is a rational function because it is a ratio of two polynomials. The denominator $x^2 + 8$ is never zero for any real x, since $x^2$ is always non-negative and adding 8 ensures the denominator is always positive. Therefore, the domain is all real numbers, $(-\infty, \infty)$.

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