The approximate rate of change of this function on the interval [-2, 2] is Option A; -9/8.
How to measure the rate of change of something as some other value changes?
Suppose that we have to measure the rate of change of y as x changes, then we have:
[tex]Rate = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
where we have
[tex]\rm when \: x=x_1, y = y_1\\when\: x = x_2, y= y_2[/tex]
Remember that, we divide by the change in independent variable so that we get some idea of how much the dependent quantity changes as we change the independent quantity by 1 unit.
The interval given as: -2 ≤ x ≤ 2
Let (x_1,y_1) = (-2, 2) and (x_2,y_2) = (2, -2.5)
The rate of change
[tex]\dfrac{y_2-y_1}{x_2-x_1}\\\\\\=\dfrac{-2.5-2}{2+2} \\\\=\dfrac{-4.5}{4}\\\\=-\dfrac{9}{8}[/tex]
Therefore, the approximate rate of change of this function on the interval [-2, 2] is Option A; -9/8.
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