Answer:
the correct answer is marked (1/2)
Explanation:
The average rate of change is the slope of the line between the two points at the ends of the interval.
m = (g(3) -g(-4))/(3 -(-4))
The values of the function we need are ...
g(3) = 5/(3-1) +2 = 2.5 +2 = 4.5
g(-4) = 5/(-4-1) +2 = -1 +2 = 1
So, the slope is ...
m = (4.5 -1)/7 = 3.5/7 = 1/2
The average rate of change is 1/2.
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On the attached graph, that value shows up as the coefficient of x in the equation of the line through the two points.