From the graph we can conclude:
For;
[tex]x<2[/tex]
The function is a parabola centered at the origin and shifted 4 units up, therefore:
[tex]y=x^2+4[/tex]
And for:
[tex]x\ge2[/tex]
The function is a line which slope is -1 and its y-intercept is 4, so:
[tex]y=-x+4[/tex]
Answer:
[tex]y=\begin{cases}x^2+4,_{\text{ }}x<2 \\ -x+4,_{\text{ }}x\ge2\end{cases}[/tex]
