1. Sit in the same seat as yesterday
WARM UP
Sit in the same seat as yesterday
1. What is a function?
2. What is a relation?
3. Is the following relation a function {(2,3), (4,7), (-2,4), (1,3)}
4. Map the following points and determine if they are a function (1,2), (-1, 3), (1, 3), (-2, 4)

2. Relations and Functions
OBJ: How to determine a domain and range given a relation or a function

3. 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) y x

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

5. 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!
FUNCTION!
NOPE!

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

7. Is this a graph of a function?
Yes No
Answer Now

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

9. Given h(z) = z2 - 4z + 9, find h(-3)
(-3)2-4(-3)+9 -3 30
h(-3) = 30

10. Given g(x) = x2 – 2, find g(4) 2 6 14 18
Answer Now

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

12. 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.

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

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

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

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

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

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

19. Let’s review tables! Graph y = 2x + 1 using the domain {0, 1, 4}
Make sure the equation is solved for y.
Create a t-table using the domain values.
Plug in the domain values and solve for the range.
Plot the points and connect them to create the line.
x y=2x+1 y 1 4
Answer Now 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

20. Let’s use the domain {0, 1, 2} for our equation.
Create a t-table by picking at least three numbers to plug into our equation.
Let’s use the domain {0, 1, 2} for our equation. x 1 2
ordered pair y
-2(0) (0, 3)
-2(1) (1, 1)
-2(2) (2, -1)