Question

WILL GIVE BRAINIEST ANSWER IF ANSWER IS CORRECT

Answer 1

F(x) = x+4
f(4) = 8, f(5) = 9
Change = 1

f(x) = 3x-7
f(-3) = -16, f(5) = 8
Change = 24/8 = 3

f(x) = 9x+1
f(-5) = -44, f(-2) = -17
Change = 27/3 = 9

f(x) = 2x+9
f(1) = 11, f(2) = 13
Change = 2

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

Answer 2

Answer::

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

$A(x) = \frac{f(b)-f(a)}{b-a}$

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;

$A_1(x) = \frac{f(5)-f(4)}{5-4} = \frac{9-8}{1} = \frac{1}{1} = 1$

Similarly for :

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

at x = -3

f(-3) = -16

At x = 7:

f(7) = 14

then;

$A_2(x) = \frac{f(7)-f(-3)}{7-(-3)} = \frac{14+16}{10} = \frac{30}{10} = 3$

For:

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

At x = -5

f(-5) = -44

At x = -2

f(-2) = -17

then;

$A_3(x) = \frac{f(-2)-f(-5)}{-2-(-5)} = \frac{-17+44}{3} = \frac{27}{3} =9$

For:

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

At x = 1

f(1) = 11

At x =2

f(2)= 13

then;

$A_4(x) = \frac{f(2)-f(1)}{2-1} = \frac{13-11}{1} = \frac{2}{1} =2$

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

$A_1 < A_4< A_2$

⇒$1< 2< 3< 9$

⇒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,