If `g (x) = (x-2)^(2)-5,` which of the following statements is true ?

Options

A. The function g (x) is increasing over the entire domain.
B. The functin g (x) is decreasing over the entire domain.
C. The function g (x) is increasing for `x lt 2` and decreasing for `x gt 2.`
D. The function g (x) is decreasing for `x lt 2` and increasing for `x gt 2.`

Answer

D

Explanation

Draw a quick sketch of the equation for graph it in your graphing calculator):

Based on the equation, the graph is a parabola that opens upward with a vertex of `(2, -5).` A parabola changes direction at the x-coordinate of its vertex. You can immediately eliminate (A) and (B). To the left of 2 on the x-axis (or `x lt2`), the parabola is decreasing, and to the right of 2 on the x-axis (or `x gt2`), it is increasing. (D) is correct.