Although you were asked to make a table of function values and then to plot these points on the graph, you could take the alternative approach of examining the terms of the given function y = +2 - x^2. Do you recognize "x^2" as the squaring function, whose graph is that of a parabola? The graph of - x^2 is the same as that of x^2, except that the whole graph of x^2 is rotated around the x-axis. Finally, that "+2" translates the whole graph of - x^2 upward by 2 units. A second degree function such as y = x^2 is definitely nonlinear.
Second question: y = 1 - x, or y = +1 - x^1:
This is linear (its graph is that of a straight line). You know that because the x term is to the first power. The graph of y = x goes thru the origin and continues to rise with x. This is the commonest graph of a linear function.
Now if we change the sign in front of x from + to - , the effect is to reflect the graph of y = x in the x-axis. The graph now decreases as x increases.
Lastly, if we add 1 to y = -x, we get y = 1 - x. The graph is the same as the previous one, except that the whole graph of y = - x is translated upward by 1 unit.
