Warm up What is the tenth term of an = 2n + 3? What is the Domain: Range: x – ints: y – int:

Review HW

Average Rate of Change

Rate of Change Ratio describing how one quantity changes as another quantity changes Slope can be used to describe it

Rate of Change Positive – increases over time Negative – decreases over time

Rate of Change Linear functions have a constant rate of change, meaning values increase or decrease at the SAME rate over a period of time

Rate of Change Horizontal lines have 0 rate of change Vertical lines have undefined rate of change

Rate of Change The slope of a non-vertical line is the ratio of the vertical change (change in y) to the horizontal change (change in x) between any two points on the line.

Rate of Change Example: Find the slope between (2, 4) and (4, 8)

Rate of Change Example: 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.

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

Average Rate of Change

Ex 1 Find the Average Rate of Change f(x) = -4x + 10 from [-1, 3]. m = -4

Ex 2 Find the Average Rate of Change f(x) = 2x2 – 3 from [2, 4].

You Try!! Find the average rate of change for f(x) = x2 + 2 from [-3, 5].

A. Find the rate of change from day 1 to 2. Ex 4 Find the Average Rate of Change A. Find the rate of change from day 1 to 2. m = 11 Days (x) Amount of Bacteria f(x) 1 19 2 30 3 48 4 76 5 121 6 192 B. Find the rate of change from day 2 to 5.

Ex 5 Find the Average Rate of Change Households in Millions f(x) In 2008, about 66 million U.S. households had both landline phones & cell phones. Find the rate of change from 2008 – 2011. Year (x) Households in Millions f(x) 2008 66 2009 61 2010 56 2011 51 m = -5 What does this mean? It decreased 5 million households per year from 2008 – 11.

Class Work Handout