4. D OMAIN & R ANGE

5. E XAMPLE 1 Find the domain and range of the relation. {(5,12.8), (10, 16.2), (15,18.9), (20, 20.7), (25, 21.8)}

6. FUNCTIONS

7. M ORE ON F UNCTIONS A function (fnc) is a relation in which no two ordered pairs have the same first component and different second components. Four Representations Verbally (in words) Numerically (table of values) Visually (a graph) Algebraically (a formula)

8. M APPING – ILLUSTRATES HOW EACH MEMBER OF THE DOMAIN IS PAIRED WITH EACH MEMBER OF THE RANGE (N OTE : L IST DOMAIN AND RANGE VALUES ONCE EACH, IN ORDER.) Draw a mapping for the following. (5, 1), (7, 2), (4, -9), (0, 2) 04570457 -9 1 2 Is this relation a function?

9. E XAMPLE 2 Determine whether each relation is a function and give the domain and range: A) {(1,2), (3,4), (5,6), (5,8)} B) {(1,2), (3,4), (6,5), (8,5)}

10. E XAMPLE 3 Determine if the given relation is a function and give the domain and range. a)b) 04 1 24 37 4-2 54 09 1 14 27 3-2 55

11. E XAMPLE 3 ( CONT.) 09 1 14 27 3-2 55

12. T HE V ERTICAL L INE T EST y x 5 5 -5 y x 5 5

13. V ERTICAL L INE T EST Graph the relation. (Use graphing calculator or pencil and paper.) Use the vertical line test to see if the relation is a function. Vertical line test – If any vertical line passes through more than one point of the graph, the relation is not a function.

14. G RAPHICALLY I DENTIFYING THE D OMAIN & R ANGE

15. y x 5 5 -5 y x 5 5 Example 4 Determine if the graph is a function and state the domain and range. a) b)

16. Example 4 (cont.) c) d) y x 5 5 -5 y x 5 5

17. Example 4 (cont.) e) f) y x 5 5 -5 y x 5 5

18. S ECTION 3.6 Function Notation and Linear Functions

19. E XAMPLE 1

20. E XAMPLE 2