Non-linear
1) Looking attentively at that table, we can see that for the points given there is no line able to intercept. Let's take a look
Apparently, this could be a conic, a parabola so not linear.
2) The fact that for x =-1, y =4 and x =1 y = 4 points out that this is also a non-linear function. Due to fact that no line could intercept x=-1 and y=4 and x=1 and y=4. Note that the extremely high value for y at x=-3.