I guess what would really help is if someone could define range for me.
I thought range was all y cordinates, so for this graph:
I guessed range was (-1, 2)
but this answer is incorrect.
The range is [-1, 2] (unless the y-coordinate of the minimum turning point is less than -1, in which case I don't see how you'd be expected to know what the value is). Square barckets include the endpoint, round brackets do not. The endpoints are included because they are labelled on the graph with a closed circle rather than an open circle.
I feel your pain (actually I don't but I thought I'd say that to make you feel better).
For the given question and graph, [-1, 2] is the reasonable and correct answer. Unless you're meant to enter it as $\displaystyle -1 \leq y \leq 2$. I suggest you flag this question with your instructor for further clarification.