Respuesta :
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]:
What is the average rate?
The average rate of change = [tex]\frac{m(b)-m(a)}{b-a}[/tex]
Where, a = -2, m(a) = -12
b = 2, m(b) = 4
Plug the values into the equation
The average rate of change
[tex]=\frac{4-(-12)}{2-(-2)} =\frac{16}{4}[/tex]
The average rate of change = 4
The average rate of change of n(x) over [-2, 2]:
The average rate of change = [tex]\frac{n(b)-n(a)}{b-a}[/tex]
Where, a = -2, n(a) = -6
b = 2, n(b) = 6
Plug the values into the equation
The average rate of change
[tex]=\frac{6-(-6)}{2-(-2)} \\=\frac{12}{4}[/tex]
The average rate of change = 3
The average rate of change of q(x) over [-2, 2]:
The average rate of change = [tex]\frac{q(b)-q(a)}{b-a}[/tex]
Where, a = -2, q(a) = -4
b = 2, q(b) = -12
Plug the values into the
The average rate of change = [tex]\frac{-4-12}{2-(-2)}[/tex]
= [tex]\frac{-16}{4}[/tex]
The average rate of change = -2
The average rate of change of p(x) over [-2, 2]:
The average rate of change = [tex]\frac{p(b)-p(a)}{b-a}[/tex]
Where, a = -2, p(a) = 12
b = 2, p(b) = -4
Plug the values into the equation
The average rate of change = [tex]\frac{-4-12}{2-(-2)}[/tex]
[tex]=\frac{-16}{4}[/tex]
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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