Question

Given the function defined in the table below, find the average rate of change, in simplest form,

of the function over the interval 20 <≤ x ≤ 35.
x
CT
5
20
35
50
f(x)
10
19
28
37

Answer 1

The average rate of change of the function over the interval 20 < x ≤ 35 is 3/5. This indicates that, on average, the function increases by 3 units for every 5-unit increase in x within the specified interval.

To find the average rate of change of a function over an interval, you can use the formula:

Average Rate of Change = (Change in f(x)) / (Change in x)

In this case, you're interested in the interval 20 < x ≤ 35, so you'll be looking at the change in f(x) and the change in x over this interval.

The change in f(x) is given by f(35) - f(20), and the change in x is 35 - 20.

Average Rate of Change = (f(35) - f(20)) / (35 - 20)

Now, let's plug in the values from the table:

Average Rate of Change = (28 - 19) / (35 - 20)

Simplify the numerator and denominator:

Average Rate of Change = 9 / 15

Now, simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 3:

Average Rate of Change = 3 / 5

So, the average rate of change of the function over the interval 20 < x ≤ 35 is 3/5.