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

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

Increasing: x 2

Increasing: x - 7

Increasing: x 7

Increasing: x > 2; decreasing: x < 2

G (x) = 2 - (x - 7) ²

g (x) = 2 - (x² - 14 x + 49)

g (x) = 2 - x² + 14 x - 49

g (x) = - x² + 14 x - 47

The maximum of the function is at:

x = - b / 2 a

x = - 14 / ( - 2) = 7

Therefore the function is increasing form x ∈ ( - ∞, 7) and decreasing for x ∈ (7, + ∞).

Answer:

C. increasing, x 7.