Answer:
Option C is correct answer.
Explanation:
We need to draw the graph of piece wise function
![f(x)\[ \begin{cases} -2-x & if\:x\leq 1 \\ -3+2x & if\: x>1 \end{cases}\]](https://img.qammunity.org/2022/formulas/mathematics/high-school/mnwbb2549zbml5k9lghvh878lhflmb2ofr.png)
So, for drawing the graph, we will find values of f(x) for both the given equations.
First finding f(x) for

The value of x must be less than or equal 1
x f(x)
1 -3
0 -2
-1 -1
-2 0
-3 1
-4 2
The graph will start from closed circle because x ≤ 1
Now, finding values of f(x) for

The value of x must be greater than 1
x f(x)
2 1
3 3
4 5
5 7
The graph will start from open circle because x> 1
Now, plotting these numbers we will get graph of Option C.
Option C is correct answer.