Answer:
this goes with steps and answer
Step-by-step explanation:
hope this helped!
The function with the greatest average rate of change is the function k(x)
<h3>How to determine the function?</h3>
The average rate of change is calculated as
![m = \frac{y_2 - y_1}{x_2 -x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-x_1%7D)
The interval is [0,2].
So, we have
![m = \frac{y_2 - y_1}{2 -0}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7B2%20-0%7D)
![m = \frac{y_2 - y_1}{2}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7B2%7D)
For function j(x), we have
j(2) = 3 * 1.6^2 = 7.68
j(2) = 3 * 1.6^0 = 3
So, we have
![m_j = \frac{7.68 - 3}{2}](https://tex.z-dn.net/?f=m_j%20%3D%20%5Cfrac%7B7.68%20-%203%7D%7B2%7D)
![m_j = 2.34](https://tex.z-dn.net/?f=m_j%20%3D%202.34)
For function g(x), we have
g(2) = 25/2
g(0) = 8
So, we have
![m_g = \frac{25/2 - 8}{2}](https://tex.z-dn.net/?f=m_g%20%3D%20%5Cfrac%7B25%2F2%20-%208%7D%7B2%7D)
![m_g = 2.25](https://tex.z-dn.net/?f=m_g%20%3D%202.25)
For function k(x), we have
k(2) = 9
k(0) = 4
So, we have
![m_k = \frac{9 - 4}{2}](https://tex.z-dn.net/?f=m_k%20%3D%20%5Cfrac%7B9%20-%204%7D%7B2%7D)
![m_k = 2.5](https://tex.z-dn.net/?f=m_k%20%3D%202.5)
For function f(x), we have
f(2) = 1.5 * 2^2 = 6
f(0) = 1.5
So, we have
![m_f = \frac{6 - 1.5}{2}](https://tex.z-dn.net/?f=m_f%20%3D%20%5Cfrac%7B6%20-%201.5%7D%7B2%7D)
![m_f = 2.25](https://tex.z-dn.net/?f=m_f%20%3D%202.25)
The function with the greatest average rate of change is the function k(x) with a rate of 2.5
Read more about average rate of change at:
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Answer:
0, 2, 4
Step-by-step explanation:
multiply 1/3 to x to get y
So for 0
0*1/3 = 0
6*1/3= 2
12*1/3= 4
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