Question

A function is given. 6 g(x) = x+7; x=0, x=h 71

(a) Determine the net change between the given values of the variable. X
(b) Determine the average rate of change between the given values of the variable. X

Answer 1

(a) The net change between the given values of the variable is:

g(h) - g(0) = h + 7 - 0 = h

(b) The average rate of change between the given values of the variable is:

average rate = (change in output) / (change in input) = (g(h) - g(0)) / (h - 0) = h / h = 1

Step-by-step explanation:

To find the net change and average rate of change between the given values of the variable, we follow these steps:

1. First, we find the values of the function at the given points:

g(0) = 6(0) + 7 = 7

g(h) = 6h + 7

2. Next, we find the net change in the function value by subtracting the value at x = 0 from the value at x = h:

g(h) - g(0) = 6h - 6(0) + 7 - 7 = h

3. To find the average rate of change, we divide the net change in output by the net change in input:

average rate = (change in output) / (change in input) = (g(h) - g(0)) / (h - 0) = h / h = 1