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

Just close this window to return to the on-line text.