Question

Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 12 < x < 48.

x f(x)
0 58
12 56
24 54
36 52
48 50

a) -1
b) -2
c) -3
d) -4

Answer 1

The average rate of change of the function over the interval 12 < x < 48 is -1/6. This is calculated by subtracting the function values at x = 48 and x = 12 and dividing by the difference in x-values over this interval.

Step-by-step explanation:

The student is asking for the average rate of change of a function represented by a table over a specific interval. The average rate of change is found by calculating the difference in the function values (f(x2) - f(x1)) over the difference in the x-values (x2 - x1), where (x1, f(x1)) and (x2, f(x2)) are points on the interval.

In this case, for the interval 12 < x < 48, we use the corresponding f(x) values from the table at x = 12 and x = 48. Thus, f(12) = 56 and f(48) = 50. Then we calculate the average rate of change as:

(f(48) - f(12)) / (48 - 12) = (50 - 56) / (48 - 12) = -6 / 36 = -1/6.