Question

What is the average rate of change of f(x), represented by the table of values, over the interval [-3, 4]? x f(x) -6 27 -3 6 -1 2 0 3 1 6 4 27

Answer 1

Answer:
The rate of change = 3

Step-by-step explanation:
The rate of change is also known as the slope of the line.
It can be calculated using the following rule:
slope =
`( y_(2) - y_(1) )/( x_(2) - x_(1) )`

We need to get the rate of change on the interval [-3,4]
From the table given, we can get our points as follows:
First point is (-3,6) representing (x₁,y₁)
Second point is (4,27) representing (x₂,y₂)

Substitute with these points in the above equation to get the rate of change (slope) as follows:
slope =
`(27-6)/(4--3) = 3`

Hope this helps :)