Compare the functions shown below in the attachment:
what is the correct order of the functions from least to greatest according to the average rate of change on the interval from x = −1 to x = 3?
f(x), g(x), h(x)
g(x), f(x), h(x)
h(x), g(x), f(x)
g(x), h(x), f(x)

The correct order of the functions from least to greatest according to the average rate of change on the interval from x = -1 to x = 3 is:

                         g(x) , f(x) , h(x)

 ( Since,

average rate of change of g(x) is:  1/2

average rate of change of f(x) is:  8

average rate of change of h(x) is:  12  )

The average rate of a function from x=a to x=b is calculated by the formula:

Here a= -1 and b=3

a)

The function f(x) is given by:

Hence, the average rate of change of f(x) is:

i.e.

i.e.

b)

The function g(x) is a straight line that passes through:

(-1,-2) and (3,0)

i.e.

g(-1)= -2

g(3)=0

i.e. the average rate of change is given by:

i.e.

i.e.

i.e.

c)

Based on the table of values we have:

h(-1)= 14

and

h(3)= 62

i.e.

i.e.

i.e.

answer: the correct answer is -32

step-by-step explanation: