1. Bell Ringer 10/30/14 1. 2.

2. Objectives The student will be able to: 1. identify the domain and range of a relation. 2. show relations as sets and mappings.

3. How about some more definitions? The domain is the set of 1st coordinates of the ordered pairs. The range is the set of 2nd coordinates of the ordered pairs. A relation is a set of ordered pairs.

4. Given the relation {(3,2), (1,6), (-2,0)}, find the domain and range. Domain = {3, 1, -2} Range = {2, 6, 0}

5. The relation {(2,1), (-1,3), (0,4)} can be shown by 1) a table. 2) a mapping. 3) a graph. xy 2 0 134134 2 0 134134

6. Given the following table, show the relation, domain, range, and mapping. x-1047 y36-13 Relation = {(-1,3), (0,6), (4,-1), (7,3)} Domain = {-1, 0, 4, 7} Range = {3, 6, -1, 3}

7. Mapping x-1047 y36-13 You do not need to write 3 twice in the range! 0 4 7 3 6

8. What is the domain of the relation {(2,1), (4,2), (3,3), (4,1)} 1.{2, 3, 4, 4} 2.{1, 2, 3, 1} 3.{2, 3, 4} 4.{1, 2, 3} 5.{1, 2, 3, 4} Answer Now

9. What is the range of the relation {(2,1), (4,2), (3,3), (4,1)} 1.{2, 3, 4, 4} 2.{1, 2, 3, 1} 3.{2, 3, 4} 4.{1, 2, 3} 5.{1, 2, 3, 4} Answer Now

10. Objectives The student will be able to: 1. To determine if a relation is a function. 2. To find the value of a function.

11. Functions A function is a relation in which each element of the domain is paired with exactly one element of the range. Another way of saying it is that there is one and only one output (y) with each input (x). f(x)f(x) x y

12. Function Notation Output Input Name of Function

13. Determine whether each relation is a function. 1.{(2, 3), (3, 0), (5, 2), (4, 3)} YES, every domain is different! f(x)f(x) 23 f(x)f(x) 30 f(x)f(x) 52 f(x)f(x) 43

14. Determine whether the relation is a function. 2. {(4, 1), (5, 2), (5, 3), (6, 6), (1, 9)} f(x)f(x) 41 f(x)f(x) 52 f(x)f(x) 53 f(x)f(x) 66 f(x)f(x) 19 NO, 5 is paired with 2 numbers!

15. Is this relation a function? {(1,3), (2,3), (3,3)} 1.Yes 2.No Answer Now

16. Vertical Line Test (pencil test) If any vertical line passes through more than one point of the graph, then that relation is not a function. Are these functions? FUNCTION! NOPE!

17. Vertical Line Test NO WAY! FUNCTION! NO!

18. Is this a graph of a function? 1.Yes 2.No Answer Now

19. Given f(x) = 3x - 2, find: 1) f(3) 2) f(-2) 3(3)-2 3 7 3(-2)-2 -2-8 = 7 = -8

20. Given h(z) = z 2 - 4z + 9, find h(-3) (-3) 2 -4(-3)+9 -330 9 + 12 + 9 h(-3) = 30

21. Given g(x) = x 2 – 2, find g(4) Answer Now 1.2 2.6 3.14 4.18

22. Given f(x) = 2x + 1, find -4[f(3) – f(1)] Answer Now 1.-40 2.-16 3.-8 4.4

23. Homework Due 11/3 Relations & Functions Page 27 Form G #1-20 all