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k0ka [10]
3 years ago
14

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?

Mathematics
1 answer:
luda_lava [24]3 years ago
5 0

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.

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