Question

Identify intervals on which the function is increasing, decreasing, or constant.

g(x) = 2 - (x - 7)2

Answer 1

The parabola opens downward because of the negative in front of the parenthesis. Therefore we are looking for the MAXIMUM value of the parabola. This is the point that the graph changes from increasing to decreasing.
The x-values are used in describing increasing and decreasing.
Increasing on the interval from -infinity to 7 and decreasing on the interval from 7 to positive infinity. There is no interval where the function is constant.