Only p(x) has an average rate of change of -4 over [-2, 2].
Find the average rate of change of each given function over the interval [-2, 2]]:
The average rate of change of m(x) over [-2, 2]:
<h3>What is the average rate?</h3>
The average rate of change = ![\frac{m(b)-m(a)}{b-a}](https://tex.z-dn.net/?f=%5Cfrac%7Bm%28b%29-m%28a%29%7D%7Bb-a%7D)
Where, a = -2, m(a) = -12
b = 2, m(b) = 4
Plug the values into the equation
The average rate of change
![=\frac{4-(-12)}{2-(-2)} =\frac{16}{4}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B4-%28-12%29%7D%7B2-%28-2%29%7D%20%3D%5Cfrac%7B16%7D%7B4%7D)
The average rate of change = 4
The average rate of change of n(x) over [-2, 2]:
The average rate of change = ![\frac{n(b)-n(a)}{b-a}](https://tex.z-dn.net/?f=%5Cfrac%7Bn%28b%29-n%28a%29%7D%7Bb-a%7D)
Where, a = -2, n(a) = -6
b = 2, n(b) = 6
Plug the values into the equation
The average rate of change
![=\frac{6-(-6)}{2-(-2)} \\=\frac{12}{4}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B6-%28-6%29%7D%7B2-%28-2%29%7D%20%5C%5C%3D%5Cfrac%7B12%7D%7B4%7D)
The average rate of change = 3
The average rate of change of q(x) over [-2, 2]:
The average rate of change = ![\frac{q(b)-q(a)}{b-a}](https://tex.z-dn.net/?f=%5Cfrac%7Bq%28b%29-q%28a%29%7D%7Bb-a%7D)
Where, a = -2, q(a) = -4
b = 2, q(b) = -12
Plug the values into the
The average rate of change = ![\frac{-4-12}{2-(-2)}](https://tex.z-dn.net/?f=%5Cfrac%7B-4-12%7D%7B2-%28-2%29%7D)
= ![\frac{-16}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B-16%7D%7B4%7D)
The average rate of change = -2
The average rate of change of p(x) over [-2, 2]:
The average rate of change = ![\frac{p(b)-p(a)}{b-a}](https://tex.z-dn.net/?f=%5Cfrac%7Bp%28b%29-p%28a%29%7D%7Bb-a%7D)
Where, a = -2, p(a) = 12
b = 2, p(b) = -4
Plug the values into the equation
The average rate of change = ![\frac{-4-12}{2-(-2)}](https://tex.z-dn.net/?f=%5Cfrac%7B-4-12%7D%7B2-%28-2%29%7D)
![=\frac{-16}{4}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B-16%7D%7B4%7D)
The average rate of change = -4
The answer is D.
Only p(x) has an average rate of change of -4 over [-2, 2].
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