Functions: Domain and Range

1. Functions: Domain and Range Y can have more than one X. X cannot have more than one Y.

2. 5-Minute Check Write the domain and range of the relation. Then determine whether each relation is a function.

3. 5-Minute Check Write the domain and range of the relation. Then determine whether each relation is a function. 1) D= {4,1,3,6}; R= {2,3,4}; yes

4. 5-Minute Check Write the domain and range of the relation. Then determine whether each relation is a function. 2) {(4,2), (-3,2), (8,2), (8,9), (7,5)}

5. 5-Minute Check Write the domain and range of the relation. Then determine whether each relation is a function. 2) {(4,2), (-3,2), (8,2), (8,9), (7,5)}

6. 5-Minute Check Write the domain and range of the relation. Then determine whether each relation is a function. 2) {(4,2), (-3,2), (8,2), (8,9), (7,5)} D={4,-3,8,7}; R= {2,9,5}; no

7. 5-Minute Check Write the domain and range of the relation. Then determine whether each relation is a function. 3) {(-3,1), (0,2), (2,4)}

8. 5-Minute Check Write the domain and range of the relation. Then determine whether each relation is a function. 3) {(-3,1), (0,2), (2,4)} D={-3,0,2}; R= {1,2,4}; yes

9. 5-Minute Check Write the domain and range of the relation. Then determine whether each relation is a function. 3) {(1,5), (1,3), (4,5)}

10. 5-Minute Check Write the domain and range of the relation. Then determine whether each relation is a function. 3) {(1,5), (1,3), (4,5)} D={1,4}; R= {5,3}; no

11. 5-Minute Check Write the domain and range of the relation. Then determine whether each relation is a function. 4) {(5,6), (-3,0), (1,1), (-3,6)}

12. 5-Minute Check Write the domain and range of the relation. Then determine whether each relation is a function. 4) {(5,6), (-3,0), (1,1), (-3,6)} D={5,-3,1}; R= {6,0,1}; no

13. 5-Minute Check Write the domain and range of the relation. Then determine whether each relation is a function. 5) {(4,2), (-3,2), (8,2), (8,9), (7,5)}

14. 5-Minute Check Write the domain and range of the relation. Then determine whether each relation is a function. 5) {(4,2), (-3,2), (8,2), (8,9), (7,5)} D={4,-3,8,7}; R= {2,9,5}; no

15. 5-Minute Check Write the domain and range of the relation. Then determine whether each relation is a function. 6) {(1,3), (-3,5), (-2,5), (2,3)}

16. 5-Minute Check Write the domain and range of the relation. Then determine whether each relation is a function. 6) {(1,3), (-3,5), (-2,5), (2,3)} D={1,-3,-2,2}; R= {3,5}; yes

17. 5-Minute Check Write the domain and range of the relation. Then determine whether each relation is a function. 7) {(3,-4), (1,0), (2,-2), (3,2)}

18. 5-Minute Check Write the domain and range of the relation. Then determine whether each relation is a function. 7) {(3,-4), (1,0), (2,-2), (3,2)} D={3,1,2}; R= {-4,0,-2,2}; no

19. 5-Minute Check Write the domain and range of the relation. Then determine whether each relation is a function. 8) {(0,4), (-3,-2), (3,2), (5,1)}

20. 5-Minute Check Write the domain and range of the relation. Then determine whether each relation is a function. 8) {(0,4), (-3,-2), (3,2), (5,1)} D={0,-3,3,5}; R= {4,-2,2,1};

21. 5-Minute Check Use the scatter plot to answer each question. 3. What kind of relationship, if any, is shown by the scatter plot? H e i g h t Weight (pounds) Weights and Heights of Basketball players

22. 5-Minute Check Use the scatter plot to answer each question. 3. What kind of relationship, if any, is shown by the scatter plot? positive H e i g h t Weight (pounds) Weights and Heights of Basketball players

23. 5-Minute Check Use the scatter plot to answer each question. 3. What kind of relationship, if any, is shown by the scatter plot? positive 4. What does the point with the triangle around it represent? H e i g h t Weight (pounds) Weights and Heights of Basketball players

24. 5-Minute Check Use the scatter plot to answer each question. 3. What kind of relationship, if any, is shown by the scatter plot? positive 4. What does the point with the triangle around it represent? 185 pound, 6’2” player H e i g h t Weight (pounds) Weights and Heights of Basketball players

25. Problem-Solving strategy - Draw a Graph Imagine you are sitting in your summer clothes and sandals eating lunch and it’s 74 degrees below zero! It happens every day on high-flying airplanes that are far from the heat of Earth’s surface.

26. Problem-Solving strategy - Draw a Graph Imagine you are sitting in your summer clothes and sandals eating lunch and it’s 74 degrees below zero! It happens every day on high-flying airplanes that are far from the heat of Earth’s surface.

27. Problem-Solving strategy - Draw a Graph Imagine you are sitting in your summer clothes and sandals eating lunch and it’s 74 degrees below zero! It happens every day on high-flying airplanes that are far from the heat of Earth’s surface. The temperature at different altitudes above sea level when the temperature at sea level is 60°F is shown in the table at the left.

28. Problem-Solving strategy - Draw a Graph Imagine you are sitting in your summer clothes and sandals eating lunch and it’s 74 degrees below zero! It happens every day on high-flying airplanes that are far from the heat of Earth’s surface. The temperature at different altitudes above sea level when the temperature at sea level is 60°F is shown in the table at the left. The table does not include an altitude for –74°. At what altitude would a jet be flying when the thermometer has this reading?

29. Problem-Solving strategy - Draw a Graph Imagine you are sitting in your summer clothes and sandals eating lunch and it’s 74 degrees below zero! It happens every day on high-flying airplanes that are far from the heat of Earth’s surface. The temperature at different altitudes above sea level when the temperature at sea level is 60°F is shown in the table at the left. The table does not include an altitude for –74°. At what altitude would a jet be flying when the thermometer has this reading? 36,000 feet

30. Problem-Solving strategy - Draw a Graph The ordered pairs (50.7, 16.47) and (99.92, 25.42) represent data from two rows of a table comparing cubic meters of natural gas used and the cost. What would the bill for 140 cubic meters of natural gas be? Plot the points and then draw a line through both points. Find 140 on the graph and then follow it to the corresponding cost.

31. Problem-Solving strategy - Draw a Graph Assignment: 6 - 17 all. Pages 398 & 399