Answer:
When we have a function:
f(x)
The average rate of change in the interval a < x < b
is given by:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
Now for each of the given intervals, let's find the average rate of changes.
q(x) = (x + 3)^2
1) -6 ≤ x ≤ -4
[tex]r = \frac{(-4 + 3)^2 - (-6 + 3)^2}{-4 - (-6)} = \frac{1 - 9}{2} = -4[/tex]
here the correct option is F.
2) -3 ≤ x ≤ 0
[tex]r = \frac{(0 + 3)^2 - (-3 + 3)^2}{0 - (-3)} = \frac{9}{-3} = -3[/tex]
Here the correct option is D.
3) -6 ≤ x ≤ -3
[tex]r = \frac{(-3 + 3)^2 - (-6 + 3)^2}{-3 - (-6)} = \frac{9}{3} = 3[/tex]
Here the correct option is C
4) -3 ≤ x ≤ -2
[tex]r = \frac{(-2 + 3)^2 - (-3 + 3)^2}{-2 - (-3)} = \frac{1}{1} = 1[/tex]
Here the correct option is B.
5) -4 ≤ x ≤ -3
[tex]r = \frac{(-3 + 3)^2 - (-4 + 3)^2}{-3 - (-4)} = -1/1 = -1[/tex]
Here the correct option is A
6) -6 ≤ x ≤ 0
[tex]r = \frac{(0 + 3)^2 - (-6 + 3)^2}{0 - (-6)} = \frac{9 - 9}{6} = 0[/tex]
Here the correct option is E.
