1. Lesson 31 Relations and Functions NCSCOS Obj.: 2.01 Daily Objectives TLW identify the domain and range of a relation. TLW show relations as sets and mappings.

2. 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.

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

4. What would this be? {(2,4), (3,-1), (0,-4)} A bad relationship!! Ha! Ha!

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. Inverse of a Relation: For every ordered pair (x,y) there must be a (y,x). Write the relation and the inverse. Relation = {(-1,-6), (3,-4), (3,2), (4,2)} Inverse = {(-6,-1), (-4,3), (2,3), (2,4)} 3 4 -6 -4 2

11. Write the inverse of the mapping. -3 4 3 2 1.{(4,-3),(2,-3),(3,-3),(-1,-3)} 2.{(-3,4),(-3,3),(-3,-1),(-3,2)} 3.{-3} 4.{-1, 2, 3, 4} Answer Now

12. 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

13. Function Notation Output Input Name of Function

14. 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

15. 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!

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

17. 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!

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

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

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

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

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

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