𝑓(𝑥) = {|𝑥| 𝑓𝑜𝑟 𝑥 < −2
     −𝑥 − 1 𝑓𝑜𝑟 − 2 ≤ 𝑥 < 2
   1/2𝑥 + 2 𝑓𝑜𝑟 𝑥 ≥ 2

On the left below is the graph of y = |x|.  On the right is the same graph
with all of it erased except the part where x < -2. And since it does
not have a value at -2, we put an open circle where x would be -2.



On the left below is the graph of y = -x-1.  On the right is the same graph
with all of it erased except the part where -2 ≤ x < 2. And since it has
a value where x = -2, we put a closed circle where x = -2.  But since
it does not have a value at 2, we put an open circle where x 
would be 2.



On the left below is the graph of y = 1/2x + 2.  On the right is the same
graph with all of it erased except the part where x ≥ 2. And since it does
have a value when x = 2, we put a closed circle where x = 2.



To get the final graph, we put all three of those graphs on the
right above all together on the same set of axes:



Edwin