Classify the function as a polynomial function, rational function, or root function, and then find the domain. Write the domain in interval notation.
-$$f ( x ) = \frac { 1 } { x ^ { 2 } + 6 x - 16 }$$
A) rational function; $( - \infty , - 8 ) \cup ( - 8,2 ) \cup ( 2 , \infty )$
B) rational function; $( - \infty , \infty )$
C) rational function; $( - \infty , 2 ) \cup ( 2 , \infty )$
D) rational function; $( - \infty , - 8 ) \cup ( - 8 , \infty )$

Question

Classify the function as a polynomial function, rational function, or root function, and then find the domain. Write the domain in interval notation.
-$$f ( x ) = \frac { 1 } { x ^ { 2 } + 6 x - 16 }$$ 
A) rational function; $( - \infty , - 8 ) \cup ( - 8,2 ) \cup ( 2 , \infty )$
B) rational function; $( - \infty , \infty )$
C) rational function; $( - \infty , 2 ) \cup ( 2 , \infty )$
D) rational function; $( - \infty , - 8 ) \cup ( - 8 , \infty )$

Quizplus · Accepted Answer

The function is a rational function because it is a ratio of two polynomials. The domain is all real numbers except where the denominator equals zero. Solving $x^2 + 6x - 16 = 0$ gives $x = -8$ and $x = 2$, so the domain is $(-\infty, -8) \cup (-8, 2) \cup (2, \infty)$.

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