1. LESSON 1–6 Relations

2. Over Lesson 1–5 5-Minute Check 1 What is the solution of 5b – 11 = 34 given the replacement set {7, 9, 13, 16, 22}?

3. Over Lesson 1–5 5-Minute Check 2

4. Over Lesson 1–5 5-Minute Check 3 Solve (6 – 42 ÷ 7) + k = 4.

5. Over Lesson 1–5 5-Minute Check 4 Solve (3 + 4 2 – 9)m = 90.

6. Over Lesson 1–5 5-Minute Check 5 Solve 8a – (15 – 3.2) = a + (5 2 – 13).

7. Over Lesson 1–5 5-Minute Check 6

8. TEKS Targeted TEKS A.2(A) Determine the domain and range of a linear function in mathematical problems; determine reasonable domain and range values for real-world situations, both continuous and discrete; and represent domain and range using inequalities. Mathematical Processes A.1(A), A.1(E)

9. Vocabulary coordinate system coordinate plane x- and y-axes origin ordered pair x- and y-coordinates relation mapping domain range independent variable dependent variable

10. Example 1 Representations of a Relation A. Express the relation {(4, 3), (–2, –1), (2, –4), (0, –4)} as a table, a graph, and a mapping. Table List the x-coordinates in the first column and the corresponding y-coordinates in the second column.

11. Example 1 Representations of a Relation Graph Graph each ordered pair on a coordinate plane.

12. Example 1 Representations of a Relation Mapping List the x-values in the domain and the y-values in the range. Draw an arrow from the x-value to the corresponding y-value. 4 –2 2 0 3 –1 –4 DomainRange

13. Example 1 Representations of a Relation B. Determine the domain and range for the relation {(4, 3), (–2, –1), (2, –4), (0, –4)}. Answer: The domain for this relation is {4, –2, 2, 0}. The range is {3, –1, –4}.

14. Example 1 A. Express the relation {(3, –2), (4, 6), (5, 2), (–1, 3)} as a mapping.

15. Example 1 B. Determine the domain and range of the relation {(3, –2), (4, 6), (5, 2), (–1, 3)}.

16. Example 2 Independent and Dependent Variables A. CLIMATE In warm climates, the average amount of electricity used rises as the daily average temperature increases, and falls as the daily average temperature decreases. Identify the independent and the dependent variables for this function. Answer: Temperature is the independent variable, as it is unaffected by the amount of electricity used. Electricity usage is the dependent variable, as it is affected by the temperature.

17. Example 2 Independent and Dependent Variables B. CALORIES The number of calories you burn increases as the number of minutes that you walk increases. Identify the independent and the dependent variables for this function.

18. Example 2 A. In a particular club, as membership dues increase, the number of new members decreases. Identify the independent and dependent variable in this function.

19. Example 2 B. The area of a square increases as the length of a side increases. Identify the independent and dependent variable in this function.

20. Example 3 Analyze Graphs The graph represents the temperature inside on a winter day. Describe what is happening in the graph. Sample answer: The temperature increases after the heat is turned on. Then the temperature fluctuates up and down because of the thermostat. Finally, the temperature drops when the heat is turned off.

21. Example 3 The graph represents Macy’s speed as she swims laps in a pool. Describe what is happening in the graph.

22. LESSON 1–6 Relations