2. (1 point) the graph of g is shown below. sketch the graph of g.

Explanation:

Step1: Identify the function type

The graph of (g(x)) is a straight - line. The general form of a straight - line function is (y = mx + b). Using two points ((0,2)) and ((1,0)), the slope (m=\frac{0 - 2}{1-0}=- 2) and the (y) - intercept (b = 2), so (g(x)=-2x + 2).

Step2: Find the first - derivative

The derivative of (g(x)=-2x + 2) using the power rule ((x^n)^\prime=nx^{n - 1}) is (g^\prime(x)=\frac{d}{dx}(-2x + 2)=-2).

Step3: Find the second - derivative

The derivative of a constant function (y = c) (where (c=-2) in the case of (g^\prime(x))) is (0). So (g^{\prime\prime}(x)=\frac{d}{dx}(-2)=0).

Answer:

The graph of (g^{\prime\prime}(x)) is a horizontal line at (y = 0) for all (x) values.