SAT Mathematics Practice Test 3

For any value of x, say $\mathit{x}={\mathit{x}}_0$,
the point $\left({\mathit{x}}_0,\mathit{f}\left({\mathit{x}}_0\right)\right)$ lies on the graph of f and the point $\left({\mathit{x}}_0,\mathit{g}\left({\mathit{x}}_0\right)\right)$ lies on the graph of g.
Thus, for any values of any value of x, say $\mathit{x}={\mathit{x}}_0$,
the value of $\mathit{f}\left({\mathit{x}}_0\right)+\mathit{g}\left({\mathit{x}}_0\right)$ is equal to the sum of the y-coordinates of the points on the graphs of f and g with x-coordinate equal to ${\mathit{x}}_0$.
Therefore, the value of x for which f(x) + g(x) is equal to 0 will occur,
when the y-coordinates of the points representing $\mathit{f}\left(\mathit{x}\right)$ and $\mathit{g}\left(\mathit{x}\right)$ at the same value of x are equidistant from the$\mathit{x}-$axis and are on opposite sides of the x-axis.
Looking at the graphs, one can see that this occurs at $\mathit{x}=-2$: the point $\left(-2,-2\right)$ lies on the graph of f, and the point $\left(-2,2\right)$ lies on the graph of $\mathit{g}$.
Thus, at $\mathit{x}=-2$, the value of $\mathit{f}\left(\mathit{x}\right)+\mathit{g}\left(\mathit{x}\right)$ is $-2+2=0$.
Choices A, C, and D are incorrect because none of these x-values satisfy the given equation, $\mathit{f}\left(\mathit{x}\right)+\mathit{g}\left(\mathit{x}\right)=0$.