Let's look at the first case: $g(x) = f(x) + c$ .
The old graph is $y = f(x)$, and the new one is $y = f(x)+c$. Thus all the $y$-coordinates in the graph of the new equation are $c$ more than those of the old equation. Since the $y$-coordinate of a point is just its height, it follows that the new graph is $c$ units higher than the old one.
Now think about what happens when $g(x) = f(x) - c$.
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