How would I graph that, what would it look like?
x-2 : -8‹X‹0
2^x : -8<x<0
-2(x-4) : 2‹X‹8
First, you obviously need the graph paper or sheet. Something with a grid.
Establish your x and y axes.
The first thing you need to do is solve for $\displaystyle y=x-2$ at -8. Then do the same at -2. I would hope that you know that x-2 is a straight line, so plug in those two coordinates on your grid and connect them. since the signs are not OR EQUAL TO (meaning that the bounds are $\displaystyle -8<x<0, not -8≤x≤0$), you need to have open circles, like this at either end of your line, like this: o
Next, you find $\displaystyle y=2^x$ for $\displaystyle x=-8 and x=0$. Plug in those two coordinates. Since this is a power function, it will be a curve. What you should do to find out how that curve fits is find $\displaystyle y=2^x$ for points in the middle, such as -6, -4, and -2, then fit the best line you can. Since these signs ARE EQUAL TO ($\displaystyle -8≤x≤0$), you need closed circles at either end, like this: •.
The last function you do the same. Plug in both ends and put open circles there. since this graph is linear, just draw a straight line between them.
Draw vertical lines in light pencil (since they won't be part of the graph) at x= -8, 0, 2, and 8.
Draw the graph of y= x- 2 (a straight line, of course) also in light pencil and erase any part of it that is to the right of the line x= -8. Draw the rest, to the left of x= -8, in dark pencil or ink.
Draw the graph of y= 2^x in light pencil. Erase that part that is to the left of x= -8 or to the right of x= 0. Draw the rest, between x=-8 and x=0, in dark pencil or pen. Also, because this section includes "-8= x" and "x= 0", mark dark "dots" at the ends of that graph.
Draw the graph of y= -2(x- 4) (again a line). Erase that part that is to the left of x= 2 and to the right of x= 8. Draw the part between x= 2 and x= 8 in dark pencil or ink. Notice that there is no graph between x= 0 and x= 2. That is because your function is not defined there.