1. 1.7 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Represent Functions as Graphs

2. 1.7 Warm-Up 1. Make a table for y = 2x + 3 with domain 0, 3, 6, and 9. 2. Write a rule for the function. ANSWER y = 3x + 1 x0369 y391521 Input, x 0249 Output, y 171328

3. 1.7 STEP 1 Make an input-output table. SOLUTION Graph the function y = x with domain 0, 2, 4, 6, and 8. 1 2 Example 1

4. 1.7 STEP 2 Plot a point for each ordered pair (x, y). Example 1

5. 1.7 Graph the function y = 2x – 1 with domain 1, 2, 3, 4, and 5. ANSWER Guided Practice

6. 1.7 The table shows the average score s on the mathematics section of the Scholastic Aptitude Test (SAT) in the United States from 1997 to 2003 as a function of the time t in years since 1997. In the table, 0 corresponds to the year 1997, 1 corresponds to 1998, and so on. Graph the function. SAT Scores Example 2

7. 1.7 SOLUTION STEP 1 Choose a scale. The scale should allow you to plot all the points on a graph that is a reasonable size. The s -values range from 511 to 519, so label the s- axis from 510 to 520 in increments of 2 units. The t -values range from 0 to 6, so label the t -axis from 0 to 6 in increments of 1 unit. STEP 2 Plot the points. Example 2

8. 1.7 WHAT IF? In Example 2, suppose that you use a scale on the s -axis from 0 to 520 in increments of 1 unit. Describe the appearance of the graph. The graph would be very large with all the points near the top of the graph. ANSWER Guided Practice

9. 1.7 Write a rule for the function represented by the graph. Identify the domain and the range of the function. SOLUTION STEP 1 Make a table for the graph. Example 3

10. 1.7 STEP 2 Find a relationship between the inputs and the outputs. Notice from the table that each output value is 1 more than the corresponding input value. STEP 3 Write a function rule that describes the relationship: y = x + 1. A rule for the function is y = x + 1. The domain of the function is 1, 2, 3, 4, and 5. The range is 2, 3, 4, 5, and 6. ANSWER Example 3

11. 1.7 Write a rule for the function represented by the graph. Identify the domain and the range of the function. 3. ANSWER y = 5 – x ; domain: 0, 1, 2, 3, and 4, range: 1, 2, 3, 4, and 5 Guided Practice

12. 1.7 Write a rule for the function represented by the graph. Identify the domain and the range of the function. ANSWER y = 5x + 5 ; domain: 1, 2, 3, and 4, range: 10, 15, 20, and 25 4. Guided Practice

13. 1.7 The graph shows guitar sales (in millions of dollars) for a chain of music stores for the period 1999–2005. Identify the independent variable and the dependent variable. Describe how sales changed over the period and how you would expect sales in 2006 to compare to sales in 2005. Guitar Sales Example 4

14. 1.7 SOLUTION The independent variable is the number of years since 1999. The dependent variable is the sales (in millions of dollars). The graph shows that sales were increasing. If the trend continued, sales would be greater in 2006 than in 2005. Example 4

15. 1.7 Yes; the graph seems to increase about $0.2 million every two years. ANSWER Based on the graph in Example 4, is $1.4 million a reasonable prediction of the chain’s sales for 2006 ? Explain. REASONING Guided Practice

16. 1.7 Lesson Quiz ANSWER Graph the function y = x + 2 with domain 2, 4, 6, and 8. 1 2 1.

17. 1.7 Write a rule for the function represented by the graph. Identify the domain and the range of the function. 2. ANSWER y = – 1 2 x + 6; Domain : 0, 2, 4, 6, 8; Range : 2, 3, 4, 5, 6 Lesson Quiz