How to find graph of the sum of two functions Suppose I know the graphs of two functions $f(x)$ and $g(x)$. How can I find the graph of $h(x)=f(x)+g(x)$? What are the rules to be followed ? 
P.S. In case my question seems silly,at least provide me with a link or something so that I can learn!
 A: You can think about the graph of $h(x)$ pointwise, adding the heights of the two graphs $f(x)$ and $g(x)$ at each point $x$. For example, if $f(1) = 2$ and $g(1) = 3$. $$h(1) = f(1) + g(1) = 2 + 3 = 5$$
Everything is all good now.
A: Since $h(x)=(f+g)(x):=f(x)+g(x)$ for every $x$ in the domain, the graph is the one that you obtain summing the two functions pointwise. 
That is, at $x=x_0$ will correspond the point $h(x_0)=f(x_0)+g(x_0)$.
Edited after seeing the comment about discontinuities: if one of the functions $f$ and $g$ has a discontinuity, remember that the domain of $f+g$ is $\mathcal {D}_{f+g}=\mathcal{D}_f \cap \mathcal{D}_g$. You can only sum the two functions where they both exists and in these points the same logic applies.
A: You need to do some analysis.I recommend take the following points.
From basic function f and g:

*

*See when are f and g zero


*Find the max and min value of the f and g (example : for sin(x) +1 and -1)


*Plot the envelopes of the shape in the enlarged size to get an idea of the graph.
OR


*Calculate the roots of function(sum) if possible.


*Analyse the value at the roots.


*Find the differential and analyze the differentiability


*Find local maxima and minimas and on the basis of differentiability plot the curve.


*You may want to analyze the concavity and convexity.For that,find the double differential.
You may like to watch this video.
Curve Sketching
