Hey man, hope your test went well.
With these types of questions you have to identify the points at which the signs inside the absolute values change, which gives you your continuos intervals. So looking at the absolute values, we see that the intervals are:
-infinity <= x < -2 , -2 <= x <= 2 , 2 < x <= 5 and: 5 < x <= infinity.
At the places where the intervals meet, there will be a "corner" of your graph, where the slope changes.
Now you just have to simplify the expression for each of these intervals by assigning values to the absolute value equations. I'll do a couple for ya, but its not really that complicated.
On the interval from -infinity to -2: (2-x) plus (-2-x) - (5-x) = y simplifies to: -x - 5 = y
On -2<x<2: (2-x) plus (x plus 2) - (5-x) = y simplifies to : -1 plus x = y
On 2<x<5: (x-2) plus (x plus 2) - (x-5) = y simplifies to : 3x - 5 = y
If you plot these, you will get a graph of your function.
I'll leave the last one for ya. The main idea is to understand where the numbers inside the absolute values change signs, and those are the intervals of continuity. This is a fairly time consuming question if you're not confident with absolute value functions.
Best of luck with the rest of your term.
Edit: fixed missing operators. Also realized that it is hard to explain these things over the internet without going into lengthly detail... sorry about the shitty explanation. Best bet is to review Absolute value functions.
