1. Unit 3: Functions Topics: Function vs. Relation
Function Notation: Part 1

2. Relation def – A relation is any set of ordered pairs.
A relation is an assignment between input values and their corresponding output values.

3. In order for a relation to be a function…
EVERY INPUT MUST HAVE AN OUTPUT
TWO DIFFERENT INPUTS CAN HAVE THE SAME OUTPUT
ONE INPUT CAN HAVE ONLY ONE OUTPUT
INPUT
(DOMAIN)
FUNCTION MACHINE
OUTPUT
(RANGE)

4. Function Notation “f of x” domain Input = x independent
Output = f(x) = y
independent
range
dependent

5. Example: Just Look & Listen
Which of the following relations are functions?
R= {(9,10), (-5, 10), (2, 10)}
S= {(6, a), (8, f), (6, b)}
T= {(z, 7), (y, -5), (r, 7) (z, 0), (k, 0)}
write this down
No two ordered pairs can have the same first coordinate
(and different second coordinates).

6. Is this a function?
1. {(2,5) , (3,8) , (4,6) , (7, 20)}
2. {(1,4) , (1,5) , (2,3) , (9, 28)}
3. {(1,0) , (4,0) , (9,0) , (21, 0)}

7. The Vertical Line Test
If it is possible for a vertical line to intersect a graph at more than one point, then the graph is NOT the graph of a function.
Page

8. Examples I’m going to show you a series of graphs.
Determine whether or not these graphs are functions.
Draw sketches of the graphs in your notes.

9. YES!
Function? #1

10. #2 Function? YES! Y = 0.5x + 2 + 2sin(x) D: all reals R: all reals
Another cool function: abs(x) + 2sin(x)

11. #3 Function? NO! Y = 0.5x + 2 + 2sin(x) D: all reals R: all reals
Another cool function: abs(x) + 2sin(x)

12. #4 Function? YES! Y = 0.5x + 2 + 2sin(x) D: all reals R: all reals
Another cool function: abs(x) + 2sin(x)

13. #5
Function?
NO!

14. YES!
Function? #6
This is a piecewise function

15. Function? #7 NO! D: all reals R: [0, 1]
Another cool function: y = sin(abs(x))
Y = sin(x) * abs(x)

16. #8 Function? NO! Y = 0.5x + 2 + 2sin(x) D: all reals R: all reals
Another cool function: abs(x) + 2sin(x)

17. YES! #9
Function?

18. Function?
#10
YES!

19. Function?
#11
NO!
D: [-3, -1) U (-1, 3]
R: {-1, 1}

20. YES!
Function?
#12
D: [-3, -1) U (-1, 3]
R: {-1, 1}