Give the domain and range for the rational function. Use interval notation.
-$$f ( x ) = \frac { 1 } { ( x + 8 ) ^ { 2 } }$$
A) Domain: $( - \infty , - 8 ) \cup ( - 8 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$
B) Domain: $( - \infty , - 8 ) \cup ( - 8 , \infty )$; Range: $( - \infty , \infty )$
C) Domain: $( - \infty , - 8 ) \cup ( - 8 , \infty )$; Range: $( 0 , \infty )$
D) Domain: $( - \infty , 8 ) \cup ( 8 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$

Question

Quizplus · Accepted Answer

The function is undefined at $x = -8$, so the domain excludes this point, making the domain $( - \infty , - 8 ) \cup ( - 8 , \infty )$. Since the function is a square of $x + 8$ in the denominator, it will always be positive for any $x$ not equal to $-8$, but it will never actually reach 0, making the range $( 0 , \infty )$.

Give the Domain and Range for the Rational Function f(x)=1(x+8)2f ( x ) = \frac { 1 } { ( x + 8 ) ^ { 2 } }f(x)=(x+8)21​

Give the Domain and Range for the Rational Function $f ( x ) = \frac { 1 } { ( x + 8 ) ^ { 2 } }$