Answer:
the average rate of change of g(x) = -18 - x between x = 1 and x = 1 + h, where h = -1.
Step-by-step explanation:
To find the average rate of change of a function g(x) between two points, we need to calculate the difference in the function values divided by the difference in the x-values.
Given:
g(x) = -18 - x
x1 = 1
x2 = 1 + h
Step 1: Find the function values at x1 and x2.
g(x1) = -18 - 1 = -19
g(x2) = -18 - (1 + h) = -18 - 1 - h = -19 - h
Step 2: Calculate the difference in function values.
Difference in function values = g(x2) - g(x1)
Difference in function values = (-19 - h) - (-19)
Difference in function values = -19 - h + 19
Difference in function values = -h
Step 3: Calculate the difference in x-values.
Difference in x-values = x2 - x1
Difference in x-values = (1 + h) - 1
Difference in x-values = h
Step 4: Calculate the average rate of change.
Average rate of change = Difference in function values / Difference in x-values
Average rate of change = (-h) / h
Simplifying the expression, we get:
Average rate of change = -1
Therefore, the average rate of change of g(x) = -18 - x between x = 1 and x = 1 + h, where h = -1.
