Find the domain and range of the function.
-$$f ( x ) = 9 - x ^ { 2 }$$
A) Domain: $( - \infty , 9 ]$; Range: $[ - 9 , \infty )$
B) Domain: $( - \infty , \infty )$; Range: $( - \infty , - 9 ]$
C) Domain: $( - \infty , \infty )$; Range: $[ 9 , \infty )$
D) Domain: $( - \infty , \infty )$; Range: $( - \infty , 9 ]$

Question

Quizplus · Accepted Answer

The domain of $f(x) = 9 - x^2$ is all real numbers because there are no restrictions on $x$, hence $(- \infty, \infty)$. The range is limited by the maximum value of $f(x)$, which occurs at $x = 0$, giving $f(0) = 9$. As $x$ increases or decreases, $f(x)$ decreases, so the range is $(-\infty, 9]$.

Find the Domain and Range of the Function f(x)=9−x2f ( x ) = 9 - x ^ { 2 }f(x)=9−x2

Find the Domain and Range of the Function $f ( x ) = 9 - x ^ { 2 }$