Finding average rate of change

The  exercise appears under the Algebra I Math Mission. This exercise calculates and applies the concept of average rate of change of functions.

Types of Problems
There are three types of problems in this exercise:


 * 1) Find the average rate of change from the graph: This problem provides a graph of a function. The student is asked to find the average rate of change over a particular interval.Aroc1.png
 * 2) Find the average rate of change from the chart: This problem provides a chart or T-table of a function. The student is asked to find the average rate of change over a particular interval.Aroc2.png
 * 3) Find the average rate of change from the function rule: This problem provides a rule for a particular function. The student is asked to find the average rate of change over a particular interval.Aroc3.png

Strategies
Knowledge of different forms of a function are useful on this exercise, but the average rate of change formula is necessary.
 * 1) The average rate of change formula is $$ frac{f(b)-f(a)}{b-a} $$.
 * 2) Average rate of change can be viewed as a slope between two points. The observation implies that slope techniques that have been developed in the past may assist on these problems.
 * 3) Horizontal lines, or places where outputs are identical, have an average rate of change of zero.

Real-life Applications

 * 1) Average rate of change is essentially the pre-derivative. It determines the rate of change of a function and so has a multitude of applications.
 * 2) The formula for average rate of change is the derivative, missing only the limit.