Pl brainliest pts for first person attached file below: select the correct function. select the function with an average rate of change of -6 over the interval [2, 4].

Function h(x)



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

If gravity is one third on mars then weight also one third on mars