# Addition and Subtraction of Functions

Addition of functions is a pointwise operation:

$(f + g)(x) = f(x) + g(x).$

Subtraction is defined similarly as

$(f - g)(x) = f(x) - g(x).$

In the applet below, the graphs of both $f\,$ and $g\,$ could be dragged up and down at any point. This will automatically change the result of the operation. The graph of $f\,$ is depicted in black and that of $g\,$ in green. For the sum $(f + g),\,$ I use blue, and for the difference $(f - g)\,$ red color. Thus of the three graphs only two -- the black and the green -- are draggable.

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