The average rate of change are as follows
1) [-5,-2] = -3
2) [-3,0] = -1
3 )[-9,7] = -1/8
4 )[-2,0] = -8
How to find the average rate of change
The average of change of the interval is solved using the formula
(y₀ - y₁) / (x₀ - x₁)
The values is gotten from the given graph.
For the interval [-5,-2]. This gives the x-values but not the y-values. We use the graph to get the y-values.
From the graph, we find the points
When x is -5, y is sought by drawing an imaginary line or tracing from -5 on the x-axis to the graph, (x₀ = -5).
Where the imaginary line intersects the graph, we trace to find the corresponding point in the y-axis.
The corresponding point is -2
Therefore, we have (-5, -2). We repeat same procedure to get for x = -2 as (-2, 7)
Average rate of change for the interval [-5,-2].
= (-2 - 7) / (-5 - (-2)
= -9 / (-5 + 2)
= -9 / 3
= -3
Average rate of change for the interval [-3,0]
From the graph: (-3, 6) (0, 3)
= (6 - 3) / (-3 - 0)
= 3 / (-3)
= -1
Average rate of change for the interval [-9,7]
From the graph: (-9, 5) (7, 3)
= (5 - 3) / (-9 - 7)
= 2 / (-16)
= -1/8
Average rate of change for the interval )[-2,0]
From the graph: (-2, -3) (0, 1)
= (-3 - 1) / (-2 - 0)
= -4 / (-2)
= -8