Question

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?

Answer 1

Answer:

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

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.  

Please have a look at the attached photo.  

My answer:

As we all know, the average of change can be determined by the following formula:

$\dfrac{f(b)-f(a)}{b-a}$

• As can be seen in the attached photo, The function f(x) is given by:

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

x = -1 we have:

 $f(-1)=(-1+3)^2-2$ = 2

x = 3 we have:

$f(3)=(3+3)^2-2$ = 34

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

$\dfrac{34-2}{3-(-1)} = 8$

• As can be seen in the attached photo, The function g(x) is a straight line that passes through: (-1,-2) and (3,0)

<=> when x = -1 y = -2 and when x = 3 y = 0

=> the average rate of change of g(x) is:

$\dfrac{g(3)-g(-1)}{3-(-1)} = \frac{1}{2}$

• Based on the table of values of h(x) we have:

h(-1)= 14

h(3)= 62

=> the average rate of change of h(x) is:

$\dfrac{62-14}{4} = 12$

Therefore,  the correct order of the functions from least to greatest according to the average rate of change is:  g(x) , f(x) , h(x)

Hope it will find you well.