Question

The function $f$ is graphed in its entirety above. If the function $g$ is defined so that $g\left(x\right)=-f\left(x\right)$, then for what value of $x$ does $g$ attain its maximum value?

• A. $-3$
• B. $-2$
• C. $0$
• D. $2$
• E. $3$

Answer 1

Answer: (B)

$-2$

As given, $y=f\left(x\right)$ ; $g\left(x\right)=-f\left(x\right)$
You can obtain the graph of $g\left(x\right)=-f\left(x\right)$ by flipping the graph of $y=f\left(x\right)$ across the y axis as shown in the figure.
For example, if point $(2,2)$ is on the graph of $f\left(x\right)$, then the point $(-2,2)$ must be on the graph of $-f\left(x\right)$.
If point $(3,1)$ is on the graph of $f\left(x\right)$, then the point $(-3,1)$ must be on the graph of $-f\left(x\right)$.
If point $(1,1)$ is on the graph of $f\left(x\right)$, then the point $(-1,1)$ must be on the graph of $-f\left(x\right)$.
If point $(-1,-1)$ is on the graph of $f\left(x\right)$, then the point $(1,-1)$ must be on the graph of $-f\left(x\right)$.
If point $(-3,-1)$ is on the graph of $f\left(x\right)$, then the point $(3,-1)$ must be on the graph of $-f\left(x\right)$.
If point $(-2,-3)$ is on the graph of $f\left(x\right)$, then the point $(2,-3)$ must be on the graph of $-f\left(x\right)$.
As we can see from the graph, $g\left(x\right)$ is maximum when $x$ $=-2$
Hence, option B is correct.