Find the range of the function.
-$$f ( x ) = ( x + 3 ) ^ { 2 } + 7$$
A) $( 7 , \infty )$
B) $( - 7 , \infty )$
C) $[ 7 , \infty )$
D) $( - \infty , \infty )$

Question

Quizplus · Accepted Answer

The function $f(x) = (x + 3)^2 + 7$ is a parabola that opens upwards with its vertex at $(-3, 7)$. The lowest value of $f(x)$ is 7, which occurs when $x = -3$. For all other values of $x$, $f(x) > 7$. Therefore, the range of $f(x)$ is $[7, \infty)$.

Find the Range of the Function f(x)=(x+3)2+7f ( x ) = ( x + 3 ) ^ { 2 } + 7f(x)=(x+3)2+7

Find the Range of the Function $f ( x ) = ( x + 3 ) ^ { 2 } + 7$