SAT Mathematics Practice Test 3

For any value of x, say $x=x_0$, the point $(x_0,f(x_0))$ lies on the graph of f and the point $(x_0, g(x_0))$ lies on the graph of g. Thus, for any values of any value of x, say $x= x_0$, the value of $f(x_0) + g(x_0)$ is equal to the sum of the y-coordinates of the points on the graphs of f and g with x-coordinate equal to $x_0$. 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 $f(x)$ and $g(x)$ at the same value of x are equidistant from the$x-$axis and are on opposite sides of the x-axis. Looking at the graphs, one can see that this occurs at $x=−2$: the point $(−2,−2)$ lies on the graph of f, and the point $(−2, 2)$ lies on the graph of $g$. Thus, at $x =−2$, the value of $f(x)+g(x)$ is $−2+2=0$.Choices A, C, and D are incorrect because none of these x-values satisfy the given equation, $f(x)+g(x)=0$.