12-3

1. 12-3 Interpreting Graphs Course 2 Warm Up Problem of the Day Lesson Presentation

2. Interpreting Graphs 12-3 Course 2 Warm Up Find a function that describes each sequence. Use the function to find the next two terms in the sequence. 1.5, 10, 15, 20 2. –7, –5, –3, –1 3. –3, –6, –9, –12 y = 5n; 25, 30 y = –9 + 2n; 1, 3 y = –3n; –15, –18

3. Interpreting Graphs 12-3 Course 2 Problem of the Day y = |x| What letter is formed by the graph of this function? V

4. Interpreting Graphs 12-3 Course 2 Learn to relate graphs to situations .

5. Interpreting Graphs 12-3 Course 2 Insert Lesson Title Here Vocabulary domain range

6. Interpreting Graphs 12-3 Course 2 You can use a graph to show the relationship between speed and time, time and distance, or speed and distance.

7. Interpreting Graphs 12-3 The graph at the right shows the varying speeds at which Emma exercises her horse. The horse walks at a constant speed for the first 10 minutes. Its speed increases over the next 7 minutes, and then it gallops at a constant rate for 20 minutes. Then it slows down over the next 3 minutes and then walks at a constant pace for 10 minutes. Course 2 20 Speed (mi/hr) 10 10 20 0 30 40 50 Time (min)

8. Interpreting Graphs 12-3 Course 2 Additional Example 1: Relating Graphs to Stories The height of a tree increases over time, but not at a constant rate. Which graph bests shows this? B. A. C. As the tree grows, its height increases and then reaches its maximum height. Graph A shows the height of a tree not increasing but remaining constant. Graph C shows the height of a tree increasing at a constant rate without reaching a maximum height. The answer is graph B.

9. Interpreting Graphs 12-3 Course 2 Insert Lesson Title Here Try This: Example 1 The dimensions of the basketball court have changed over the years. However, the height of the basket has not changed. Which graph bests shows this? C. A. B. Graph A shows the height of the basket remaining constant. Graph C shows the height increasing without reaching a maximum height. Graph B shows the height increasing at a slowing rate over time. The answer is graph A.

10. Interpreting Graphs 12-3 Helpful Hint Some graphs are curves or lines that show continuous data. Other graphs may show only points. Course 2

11. Interpreting Graphs 12-3 Course 2 Additional Example 2: Using a Graph to Tell a Story Draw a graph for each situation. A. For every packet of 10 business flyers Joel delivers, he is paid $3.00. He is not paid for delivering partial packets. Draw a graph to show how much money Joel can earn. Each packet is $3, so the amount of money he can make is a multiple of $3. The graph is only points.

12. Interpreting Graphs 12-3 Course 2 Additional Example 2B: Using a Graph to Tell a Story B. Angie has a job as a clerk at a grocery store. She earns $9.50 per hour. Draw a graph to show how much money Angie earns. In one hour she earns $9.50, in two hours she earns $19.00, and so on. However, she can work any part of an hour. This graph is continuous.

13. Interpreting Graphs 12-3 2000 1800 1600 1400 1200 Earnings ($) 1000 800 600 400 200 1 2 3 4 5 6 7 8 9 10 Number of cars sold Course 2 Insert Lesson Title Here Try This: Example 2A Draw a graph for each situation. A. For every car, the salesman sells he is paid $200.00. Draw a graph to show how much money the salesman can earn if he sells 10 cars. Each car is worth $200, so the amount of money he can make is a multiple of $200. The graph is only points.

14. Interpreting Graphs 12-3 100 80 60 Earnings ($) 40 20 2 4 6 8 10 Hours Course 2 Insert Lesson Title Here Try This: Example 2B B. Darla has a job at a fast food restaurant. She earns $6.50 per hour. Draw a graph to show how much Darla earns. In one hour she earns $6.50, in two hours she earns $13.00, and so on. However, she can work any part of an hour. This graph is continuous.

15. Interpreting Graphs 12-3 Helpful Hint When a graph is continuous, its domain and range contain all real numbers or those within a certain interval. Course 2 The set of input values of a function is the domain, and the set of resulting output values is the range. In the graph of packet delivered (Additional Example 2A), the domain is the possible number of packets delivered, or the set of whole numbers. The range in this graph is Joel’s possible income, or all nonnegative multiples of two.

16. Interpreting Graphs 12-3 Course 2 Additional Example 3: Finding Domain and Range Find the domain and range of the graph. The graph goes between 2 and 10 on the x-axis and between 1 and 8 on the y-axis. Domain: all real numbers from 2 through 10; 2 ≤ x ≤ 10 Range: all real numbers from 1 through 8; 1 ≤ y ≤ 8

17. Interpreting Graphs 12-3 Course 2 Insert Lesson Title Here Try This: Example 3 Find the domain and range of the graph. y 80 The graph goes between 2 and 8 on the x-axis and between 20 and 70 on the y-axis. 60 40 20 x 1 2 3 4 6 7 8 9 5 10 Domain: all real numbers from 2 through 8; 2 ≤ x ≤ 8 Range: all real numbers from 20 through 70; 20 ≤ y ≤ 70

18. Interpreting Graphs 12-3 Course 2 Insert Lesson Title Here Lesson Quiz: Part 1 1. What relationship does this graph show? A ball is tossed into the air. Height Time The ball’s height increases until gravity gradually stops the ball; then its height decreases in a mirror image of the ascent.

19. Interpreting Graphs 12-3 25 15 Earnings ($) 5 2 3 4 5 6 1 7 Decorated balls sold Course 2 Insert Lesson Title Here Lesson Quiz: Part 2 2. Samantha sells decorated ornamental balls for $4 each. Draw a graph to show how much she can make if she can sell up to 7 balls. 3. Name the domain and range of the graph in problem 2. Domain: all whole numbers from 0 to 7 Range: multiples of 4 from 0 to 28