Answer
False.
Work Step by Step
The lowest value that f has is at $x=-4$, where $f(-4)=-2.$
There is no highest value for f(x), because the point $(-1,2)$ does not belong to the graph.
The function values of x to the left of $x=-1$ get close to, but never reach 2....
The range is $[-2,2)$
(right border is open, not closed)
