LO­8 Average Rate of Change.notebook
LO­8: I can find the average rate of change of linear functions and exponential functions.
Key Points: Rate of Change
• The rate of change is the ratio of the change of one quantity to a change in another quantity.
• Positive ­ increasing function (rising from left to right)
• Negative ­ decreasing function (falling from left to right)
• Which function has a constant rate of change? _________________________________
• Horizontal Lines­ _________________________________________________________
• Vertical Lines ­___________________________________________________________
Constant Rate of Change
• The slope of a non­vertical line is the ratio of the vertical (change in y) to the horizontal (change in x) between any two points on the line.
Example 1: Find the slope between (2, 4) and (4, 8).
Example 2: The table shows the amount of water evaporating from a swimming pool on a hot day. Find the rate of change between 2 hours and 6 hours.
Example 3: Where is the greatest rate of change on the graph? What is the value?
The average rate of change between any two points is the slope of the line through the 2 points,
. Steps to find average rate of change:
1. Recognize that the interval given is made up of x­values.
2. Find the corresponding y­values for each x­value.
3. Write the information from Steps 1 and 2 as ordered pairs.
4. Use the slope formula to find the average rate of change.
Example 1: The graph below represents the amount of an element in grams that remains after a period of time. What is the approximate rate of change for the function for the interval [0, 2.5]? Step 1: The interval [0, 2.5] (0, ____) and (2.5, ____)
Step 2: From the graph, when x is 0, y = ________. And when x is 2.5, y = ________.
Step 3: Write as ordered pairs: (0, ______) and (2.5, _____)
Step 4: Substitute in to the slope formula:
y2 ­ y1
m=
x2 ­ x1
Example 2: Find the average rate of change for f(x) = ­4x + 10 from [­1, 3].
LO­8 Average Rate of Change.notebook
Worktime:
1. Find the average rate of change for f(x) = 2x2 – 3 from [2, 4].
2. Find the rate of change for the following using the table.
a. Find the rate of change from day 1 to 2.
b. Find the rate of change from day 2 to 5.
Days (x)
Amount of Bacteria f(x)
1
19
2
30
3
48
4
76
5
121
6
192
3. The graph below represents the cost to rent mini­bikes over a period of time. What is the approximate rate of change for the function?