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 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 ), you need to have open circles, like this at either end of your line, like this: o
Next, you find for . 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 for points in the middle, such as -6, -4, and -2, then fit the best line you can. Since these signs ARE EQUAL TO ( ), 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.