Find the domain and range of the function.
$f ( x ) = - x ^ { 2 } - 12 x - 43$
A) $\text { Domain: } ( - \infty , \infty ) \text {; Range: } ( - \infty , 6 ]$
B) $\text { Domain: } ( - \infty , \infty ) \text {; Range: } [ 7 , \infty )$
C) $\text { Domain: } ( - \infty , \infty ) \text {; Range: } ( - \infty , - 7 ]$
D) $\text { Domain: } ( - \infty , - 7 ] ; \text { Range: } [ 6 , \infty )$

Question

Quizplus · Accepted Answer

The domain of a quadratic function is all real numbers, $(- \infty, \infty)$. The range is determined by the vertex of the parabola. The vertex form of the function is $f(x) = -(x + 6)^2 - 7$, so the maximum value is $-7$. Thus, the range is $(-\infty, -7]$.

Find the Domain and Range of the Function f(x)=−x2−12x−43f ( x ) = - x ^ { 2 } - 12 x - 43f(x)=−x2−12x−43

Find the Domain and Range of the Function $f ( x ) = - x ^ { 2 } - 12 x - 43$