Graph x-4 if x<2 and -2x+2 if x > or = to 2

Answer 1

Basically, you just want to consider both functions independently.

Looking at the first one, x-4 for values less than 2 is just a straight line with positive one slope passing through the y-axis at -4. Notice that this line arrives at (2, -2), but does not include it.

Then, for x = 2 and greater, we have a straight line with a negative two slope that would have passed through the y-axis at positive two (but x=0 is not included in this function). Notice that this line originates at (2, -2) and does include it.