Question

Let $f\left(x\right)=-x^2/2$. If the graph of $f\left(x\right)$ is translated $2$ units up and $3$ units left and the resulting graph is that of $g\left(x\right)$, then $g\left(1/2\right)=$

• A. $0$
• B. $-1/8$
• C. $-2/8$
• D. $-33/8$
• E. $13/8$

Answer 1

The correct option is D $-33/8$

Translated $2$ units up

$\Rightarrow y-2=-\frac{x^2}{2}-\left(1\right)$

$\left(1\right)$ is transmiited $3$ units to left

$\Rightarrow y-2=-\frac{{(x+3)}^2}{2}$

$g\left(\frac{1}{2}\right)=\frac{{-(\frac{1}{2}+3)}^2}{2}+2=-\frac{-33}{8}$