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arrange these functions from the least to the greatest value based on the average rate of change in the specified interval. tiles f(x) = x + 4 over the interval [4, 5]f(x) = 3x − 7 over the interval [-3, 7]f(x) = 9x + 1 over the interval [-5, -2]f(x) = 2x + 9 over the interval [1, 2]

:

Average rate of change(A(x)) of f(x) over the interval [a, b] is given by:

As per the statement:

Given :

f(x) = x+4 over the interval [4, 5]

At x = 4

f(4) = 8

at x = 5

f(5) = 9

Using the above formula: we have;

Similarly for :

f(x) = 3x-7 over the interval [-3, 7]

at x = -3

f(-3) = -16

At x = 7:

f(7) = 14

then;

For:

f(x) = 9x + 1 over the interval [-5, -2]

At x = -5

f(-5) = -44

At x = -2

f(-2) = -17

then;

For:

f(x) = 2x + 9 over the interval [1, 2]

At x = 1

f(1) = 11

At x =2

f(2)= 13

then;

We have to Arrange these functions from the least to the greatest value based on the average rate of change in the specified interval.

⇒

⇒x+4 < 2x + 9 <  3x-7 < 9x + 1

Therefore, the least to the greatest value based on the average rate of change in the specified interval is:

f(x) = x+4, f(x) = 2x+9, f(x) = 3x-7, f(x) = 9x+1,

answer: 12

step-by-step explanation: