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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:

$$\mathrm{Use\ the \ graph \ to \ find \ }f(0)+g(0).$$ enter image description here

Robert Howard
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Lex_i
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1 Answers1

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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 $D_f\cap D_g = [-4,3]$

David P
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  • g contains 9 y-values and f contains 8 y-values. What am I supposed to do with the extra y-value? Or am I supposed to only count y-values within certain bounds? – Lex_i Oct 11 '18 at 07:03
  • It will only exist from $-4$ to $3$ – David P Oct 11 '18 at 15:00
  • Ah I see. So I have my new line but I am still not sure what then the sum is – Lex_i Oct 11 '18 at 16:04
  • as others said first you have to find the parts in which both functions exist which is [-4,3] and then you have to add the values of each function and put the new point on the graph. for g(0) and f(0) it is (0-2)=-2 and also you have to do this for each point and graph whole function of h(x)=f(x)+g(x) – infinite Nov 22 '20 at 06:13