I have tried looking for tutorials or guides online, but I keep finding problems that are fairly similar but not exactly what I am looking for. I know how to add functions regularly, I am familiar with graphing an equation using its slope and $y$-intercept, etc., but I have no idea where to begin on finding the sum of two functions using this graph:
$\endgroup$ 2$$\mathrm{Use\ the \ graph \ to \ find \ }f(0)+g(0).$$
1 Answer
$\begingroup$Add the $y-$ values of each of the points, while keeping the $x-$values the same to get the new point for the function $(f+g)(x)$.
One thing I did not see mentioned is that the domains do not coincide. The function $(f+g)(x) = f(x)+g(x)$ can not exist where one of them does not. The domain of the function $(f+g)(x)$ is the intersection of the two domains (or "overlap"), and domain of $f$ and $g$ intersect on $D_f\cap D_g = [-4,3]$
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