Find the set of values of the function y = x ^ 2-2 defined on the segment [-1; 3]

1. The graph of this function is a parabola, the branches of which are directed upwards, and the vertex is at the point (0; -2).

2. The abscissa of the vertex of the parabola belongs to the specified interval [-1; 3], therefore, the smallest value of the function on this interval is equal to the ordinate of the parabola, and the largest value will be at the most distant end of the segment:

y = x ^ 2 – 2;
ymin = -2;
ymax = y (3) = 3 ^ 2 – 2 = 9 – 2 = 7.
3. Thus, the set of values of the function on the segment [-1; 3] there will be a gap [-2; 7].

Answer: [-2; 7].