Answer: Function h(x)

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Explanation:

To compare the average rate of change (AROC) for the three functions, we'll use the formula

AROC = (p(a) - p(b))/(a-b)

where p(x) is any general function and [a,b] is the interval we care about. In this case, a = 2 and b = 4.

For f(x), we have
f(x) = (-5/2)*(3)^x
f(2) = (-5/2)*(3)^2
f(2) = -22.5
--------
f(x) = (-5/2)*(3)^x
f(4) = (-5/2)*(3)^4
f(4) = -202.5
--------
AROC = (f(a)-f(b))/(a-b)
AROC = (f(2)-f(4))/(2-4)
AROC = (-22.5-(-202.5))/(2-4)
AROC = -90
So we can rule out function f as the AROC here is -90 but we want the AROC to be -6

For g(x) we have
AROC = (g(a)-g(b))/(a-b)
AROC = (g(2)-g(4))/(2-4)
AROC = (-5-(-77))/(2-4)
AROC = -36
So we can rule out g(x) as well

For h(x) we have
AROC = (h(a)-h(b))/(a-b)
AROC = (h(2)-h(4))/(2-4)
AROC = (0-(-12))/(2-4)
AROC = -6
h(x) is the function that has the proper AROC we want

So that's why h(x) is the only answer

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