Question

Given the function with f(3) = 127 and f(1) = 95. Determine the rate of change over the interval 1 is greater than or equal to x is greater than or equal to 3.

A: 1/32
B: 32
C: 16
D: 1/16

Answer 1

The rate of change of the function f(x) over the interval from x = 1 to x = 3 is 16, calculated by dividing the change in function values by the change in x values (32 / 2).

Step-by-step explanation:

The student is asking to determine the rate of change of a function f(x) over an interval where x ranges from 1 to 3. Given f(3) = 127 and f(1) = 95, we calculate the rate of change by finding the difference in the function values divided by the difference in the x values. This is sometimes referred to as the average rate of change or the slope of the line connecting the points (1, f(1)) and (3, f(3)) on the graph of f(x).

The calculation is as follows:

1. Find the difference in y values: f(3) - f(1) = 127 - 95 = 32.
2. Find the difference in x values: 3 - 1 = 2.
3. Divide the difference in y values by the difference in x values to get the rate of change: 32 / 2 = 16.

Therefore, the rate of change over the interval from x = 1 to x = 3 is 16.