2A.3. Domain and Rate of Change
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1 2A.3 Domain and Rate of Change
2 2A.3 Objectives By the end of the lesson you will be able to Determine the domain of a function Find and compare the average rate of change
3 Vocabulary Domain All input values that satisfy the function without restriction. Application problems can change the domain. Layman s terms: What am I allowed to plug in? (INPUT) Ex: 3x + 7 Is there any x that does not work to plug in?
4 Vocabulary Domain All input values that satisfy the function without restriction. Application problems can change the domain. Layman s terms: What am I allowed to plug in? (INPUT) Ex: 3x + 7 Is there any x that does not work to plug in? = 37 for x = = for x = = 6.7 for x = 0.1
5 Warm Up (Domain) Tina works in a video game store. She earns $8 an hour plus commission for each video game or accessory she sells. She makes $3 commission for each game sold. Q1: What is a reasonable domain for this situation?
6 Warm Up (Domain) Tina works in a video game store. She earns $8 an hour plus commission for each video game or accessory she sells. She makes $3 commission for each game sold. Q1: What is a reasonable domain for this situation? A: Whole numbers (ex: 0,1,2,3, ). It doesn t make sense to sell a negative number of games, nor does it make sense to sell parts (fractions/decimals) of a game.
7 Guided Practice #1 (Domain) Using a graphing calculator, graph: g x = 1.5x
8 Guided Practice #1 (Domain) Using a graphing calculator, graph: g x = 1.5x Q1: What happens if we make the window bigger?
9 Guided Practice #1 (Domain) Using a graphing calculator, graph: g x = 1.5x Q1: What happens if we make the window bigger? Q2: What is the domain/ input?
10 Guided Practice #1 cont. (Domain) Experiment with quadratic graphs (x ) similar to the previous example of g x = 1.5x. Can you come up with an example with a different domain? Why or why not?
11 Guided Practice #3 (Domain) A diver on a swim team is practicing by jumping off a 14 ft platform into a pool. His height in feet above the water is modeled by f x = 16x + 14 where x is the time in seconds after he leaves the platform. How long will it take to reach the water? Q1: Sketch a graph using a graphing calculator.
12 Guided Practice #3 (Domain) A diver on a swim team is practicing by jumping off a 14 ft platform into a pool. His height in feet above the water is modeled by f x = 16x + 14 where x is the time in seconds after he leaves the platform. How long will it take to reach the water? Q1: Sketch a graph using a graphing calculator. Q2: Identify the x-intercepts.
13 Guided Practice #3 (Domain) A diver on a swim team is practicing by jumping off a 14 ft platform into a pool. His height in feet above the water is modeled by f x = 16x + 14 where x is the time in seconds after he leaves the platform. How long will it take to reach the water? Q1: Sketch a graph using a graphing calculator. Q2: Identify the x-intercepts. Q3: Use x-intercepts and story context to provide a reasonable domain.
14 Vocabulary Average Rate of Change The rate of change between any two points of a function Layman s terms: a measure of how a quantity changes over some interval Formula f b f a b a f(b) means plug b in to your function f. What number did you get back? f(a) means plug a in to your function f. What number did you get back?
15 Linear vs. Non-Linear (Average Rate of Change) Linear Non-Linear Pick two points on a graph. Using that same graph, pick two NEW points. Did your rate of change differ? Why or why not? Try this with both graphs.
16 Scaffold Practice (Average Rate of Change) Example 1: Calculate the average rate of change for the function f x = x + 6x + 9 between x = 1 and x = 3 1) Evaluate the function for x = 3
17 Scaffold Practice (Average Rate of Change) Example 1: Calculate the average rate of change for the function f x = x + 6x + 9 between x = 1 and x = 3 1) Evaluate the function for x = 3 2) Evaluate the function for x = 1
18 Scaffold Practice (Average Rate of Change) Example 1: Calculate the average rate of change for the function f x = x + 6x + 9 between x = 1 and x = 3 1) Evaluate the function for x = 3 2) Evaluate the function for x = 1 3) Use the average rate of change formula to determine the average rate of change between x = 1 and x = 3. REMINDER:
19 Example 2 (Average Rate of Change) Use the graph of the function to calculate the average rate of change between x = 3 and x = 2.
20 Example 4 (Average Rate of Change) Find the average rate of change between x =.075 and x = 0.25 for the following function.
21 Task (Average Rate of Change) A kicker for a football team can model his field goal kick by the function h t = 16x + 32x where h(t) is the height of the ball in feet t seconds after it is kicked. Can the football clear a 17 ft goalpost? What is the average rate of change of the football s height from the moment it reaches its maximum height to the moment it hits the ground?
22 Homework WB: Practice (page 127) #1-4, 8-10 Practice (page 139) #1-10 all AND answer the following question: Q. How does the rate of change of a linear equation (straight line) differ from the rate of change of a quadratic equation (parabola)?
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