Answer:
To find the average rate of change of a function over an interval, you can use the formula:
average rate of change = [f(b) - f(a)] / (b - a)
where a and b are the endpoints of the interval.
In this case, you have the function g(x) = log2(x + 3) - 4 and the interval [-2, 5]. So, plugging in the values, you get:
average rate of change = [g(5) - g(-2)] / (5 - (-2))
First, let's evaluate g(5) and g(-2).
g(5) = log2(5 + 3) - 4 = log2(8) - 4 = 3 - 4 = -1
g(-2) = log2((-2) + 3) - 4 = log2(1) - 4 = 0 - 4 = -4
Now you can substitute these values into the formula:
average rate of change = (-1 - (-4)) / (5 - (-2))
= 3 / 7
And the average rate of change of g(x) over the interval [-2, 5] is 3/7.