1. ## Adding and Dividing Piecewise Functions and their Domains?

IMG_4971.jpg
We have these two graphs, and these two functions:
A) (F+G)(x)
and
B) (F/G)(x).

And the question is asking what the domains of these two functions are. I am having a lot of trouble understanding how to get to the proper answers. If anybody could explain this question I would be very grateful.

A) (-∞, -1]u(1,2]u(3,∞)
and
B) (-∞,-4)u(-4,-1]u(1,2]u(3,∞)

2. Some general guidelines:

1) If something isn't in BOTH functions, it cannot be in the SUM.
2) Division offers an additional complication. If your denominator is zero (0), at any point, you'll have to think harder about that point.

3. If I were doing this exercise, I would begin by focusing on the endpoints of the lines shown, in the graphs of piecewise functions F(x) and G(x).

I would label their coordinates. For each of these values of x, I would then calculate F+G.

Next, I would carefully plot the F+G points calculated above, using graph paper. This would give me a visual aid to look at, going forward to consider what's happening at other values of x. And that, in turn, would help me to see where F+G exists (i.e., for which values of x it exists) and where it doesn't.