Answer:
option d
Step-by-step explanation:
We are given with three function
Plug in x=-2 in first function
f(x)= 3 so f(-2) = 3
Plug in x=-2 in second function
![f(x) = -\frac{x}{2} +2](https://tex.z-dn.net/?f=f%28x%29%20%3D%20-%5Cfrac%7Bx%7D%7B2%7D%20%2B2)
![f(-2) = -\frac{-2}{2} +2=3](https://tex.z-dn.net/?f=f%28-2%29%20%3D%20-%5Cfrac%7B-2%7D%7B2%7D%20%2B2%3D3)
Plug in x=2 in second function
![f(x) = -\frac{x}{2} +2](https://tex.z-dn.net/?f=f%28x%29%20%3D%20-%5Cfrac%7Bx%7D%7B2%7D%20%2B2)
![f(-2) = -\frac{2}{2} +2=1](https://tex.z-dn.net/?f=f%28-2%29%20%3D%20-%5Cfrac%7B2%7D%7B2%7D%20%2B2%3D1)
Plug in x=2 in third function
f(x)= 2x-3
f(2)= 2(2) -3 = 1
We can see that f(-2)=3 is same for first and second function
also f(2) = 1 is same for second and third functions
So the graph is continuous
option D satisfies the points