It's the 4th option.
Observing the oblique straight line for x < -2, we see its slope is 1.
Extend the straight line, and it meets y-axis at (0,5).
Therefore when x < -2, f(x) = x + 5.
On the other hand, when x >= -2, it is a horizontal straight line with y-intercept 4.
Therefore when x >= -2, f(x) = -4.
This is why the 4th option is the answer.