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:
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
- As can be seen in the attached photo, The function f(x) is given by:
[tex]f(x)=(x+3)^2-2[/tex]
x = -1 we have:
[tex]f(-1)=(-1+3)^2-2[/tex] = 2
x = 3 we have:
[tex]f(3)=(3+3)^2-2[/tex] = 34
Hence,the average rate of change of f(x) is:
[tex]\dfrac{34-2}{3-(-1)} = 8[/tex]
- 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:
[tex]\dfrac{g(3)-g(-1)}{3-(-1)} = \frac{1}{2}[/tex]
- 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:
[tex]\dfrac{62-14}{4} = 12[/tex]
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.
