Question

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)

Answer 1

I got 12.

f(x) = (x+3)^2 - 2 Plug in -1 for x to find the value. Plug in 3 for x to find that value.

For x = -1 I got the point (-1, 2). Let me check the second one reaFor x = 3, I got the point (3, 34). Now do I do the same thing I did before by subtracting the points, like in the formula you posted earlier

So the answer would be B,

Answer 2

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 )

Explanation:

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

`\text{Average rate of change}=(f(b)-f(a))/(b-a)`

Here a= -1 and b=3

a)

The function f(x) is given by:

`f(x)=(x+3)^2-2`

`f(-1)=(-1+3)^2-2\\\\i.e.\\\\f(-1)=2^2-2\\\\i.e.\\\\f(-1)=4-2\\\\i.e.\\\\f(-1)=2`

`f(3)=(3+3)^2-2\\\\i.e.\\\\f(3)=6^2-2\\\\i.e.\\\\f(3)=36-2\\\\i.e.\\\\f(3)=34`

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

`\text{Average rate of change}=(34-2)/(3-(-1))`

i.e.

`\text{Average rate of change}=(32)/(4)`

i.e.

`\text{Average rate of change}=8`

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:

`\text{Average rate of change}=(g(3)-g(-1))/(3-(-1))`

i.e.

`\text{Average rate of change}=(0-(-2))/(4)`

i.e.

`\text{Average rate of change}=(2)/(4)`

i.e.

`\text{Average rate of change}=(1)/(2)`

c)

Based on the table of values we have:

h(-1)= 14

and

h(3)= 62

`\text{Average rate of change}=(h(3)-h(-1))/(3-(-1))`

i.e.

`\text{Average rate of change}=(62-14)/(4)`

i.e.

`\text{Average rate of change}=(48)/(4)`

i.e.

`\text{Average rate of change}=12`