Answer:
Option A.
Step-by-step explanation:
The given piecewise function is
[tex]y=\begin{cases}x+3 & \text{ if } x<0 \\2x & \text{ if } x\geq 0\end{cases}[/tex]
We need to find the graph of given function.
For [tex]x<0, f(x)=x+3[/tex], so the table of values is
x y
-1 2
-2 1
-3 0
Because x<0, so for this piece of function there is an open circle at x=0.
For [tex]x\geq 0, f(x)=x+3[/tex], so the table of values is
x y
0 0
1 2
2 4
Because [tex]x\geq 0[/tex], so for this piece of function there is a close circle at x=0, i.e., (0,0).
Only graph A passes through the points, which are mentioned in the above tables.
Therefore, the correct option is A.
