2. given the graph of g(x) below, which points would you use to find the average rate of change between g(0)…

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function (y = g(x)) over the interval ([a,b]) is (\frac{g(b)-g(a)}{b - a}). Here (a = 0) and (b=4), so we need two points ((x_1,y_1)) and ((x_2,y_2)) such that (x_1 = 0) and (x_2=4).

Step2: Identify the points from the graph

From the graph, when (x = 0), (g(0)=- 2) (the point ((0,-2))) and when (x = 4), assume we can find the corresponding (y)-value. But since the function is linear (a straight - line graph), we can use two well - defined points. Wait, no, the problem is to select the points for (x = 0) and (x = 4). The point for (x = 0) is ((0,-2)) and we need to find the point for (x = 4). However, if we use the concept of the average rate of change formula (\frac{g(4)-g(0)}{4 - 0}), we need the values of (g(0)) and (g(4)) which correspond to the points ((0,g(0))) and ((4,g(4)))

Answer:

The points ((0,-2)) and ((4,g(4))) (where (g(4)) is the (y) - value of the function (g(x)) at (x = 4)) should be used. So we would use the point ((0,-2)) (since (g(0)=-2)) and the point ((4,g(4))) to calculate the average rate of change.