Warm-up Find the slope y x Run=6-2=4 Rise=3-1=2 = (2,1) (6,3)

Find the slope

Math I UNIT QUESTION: How do we graph functions, and what can be done to change the way they look? Standard: MM1A1 Today’s Question: How do we find the rate of change of a function? Standard: MM1A1g

Constant Rate of Change The slope of a nonvertical line is the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. The slope of a nonvertical line is the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. Find the slope between (2, 4) and (4, 8). Find the slope between (2, 4) and (4, 8).

Rate of Change The rate of change is the ratio of the change of one quantity to a change in another quantity. The rate of change is the ratio of the change of one quantity to a change in another quantity. Example: Example: - The table shows the amount of water evaporating from a swimming pool on a hot day. Find the rate of change in gallons with respect to time.

Rate of Change Where is the greatest rate of change on the graph? What is the value? Where is the greatest rate of change on the graph? What is the value?

Partner Practice Calculating rate of change from a table. Calculating rate of change from a table. Example 4 Example 4 Example 5 Example 5

Average Rate of Change The average range of change between any two points (x 1,f(x 1 )) and (x 2,f(x 2 )) is the slope of the line through the 2 points. The average range of change between any two points (x 1,f(x 1 )) and (x 2,f(x 2 )) is the slope of the line through the 2 points.

Example 1 Find the average rate of change of f(x) = 2x 2 – 3 when x 1 = 2 and x 2 = 4. Find the average rate of change of f(x) = 2x 2 – 3 when x 1 = 2 and x 2 = 4.

Example 2 Find the average rate of change of f(x) = x 3 – 3x for -2 < x < 0. Find the average rate of change of f(x) = x 3 – 3x for -2 < x < 0.

Class work p. 72 #9-13 p. 72 #9-13