Remark
That was well worth doing. Desmos gave you the answer to the graph. Unfortunately I can only give you the correct graph. You will have to figure out from the choices which one is the correct answer -- or edit it so I can see what the rest of the question is.
Graph
The red one is f(x) is x + 3 {x <= -2}
The blue one is f(x) is x^2 - 1 {-2 <x <1} Notice the gap at 2. It is not continuous
The green one is f(x) is log_2(-x + 3) {1 <=x < 3} and there is a gap between the blue and green one.