1. **Each input can match up to only one output
Functions:
Functions have EXACTLY ONE output for each input –
**Each input can match up to only one output
Examples:
ATM Vending Machine Key – Lock
Gas Station Calculator Remote Control
Pencil Sharpener Phone Keyboard
CD Player Oven

2. INPUT / OUTPUT
INPUT: The value substituted into an expression or function
OUTPUT: The value that results from the substitution of a given input into an expression or function.

3. *MAPPING*
Function:
Non-Function:

4. Mapping: “left” is the input, and “right” is the output
Tia
Shay
Sam
Joe
Tom
Swim
Cheer
Football
Basketball
Piano 6 12 18 18 36 54 4 8 12 15
Functions have EXACTLY ONE output for each input

5. Mapping: “left” is the input, and “right” is the output
Not a Function: 18 has 2 outputs
Tia
Shay
Sam
Joe
Tom
Swim
Cheer
Football
Basketball
Piano 6 12 18 18 36 54 4 8
Function: each input has only 1 output 12 15
Not a Function:
Tia and Tom have 2 outputs each
Functions have EXACTLY ONE output for each input

6. *TABLES*
Function:
Non-Function:

7. “x” is the input, and “y” is the output.
Tables:
“x” is the input, and “y” is the output.
For a table to represent a function, a number can show up in the x column only one time (input), but in the y column many times (output). x y 2 8 3 9 5 10 4 11 x y 1 3 2 10 4
Functions have EXACTLY ONE output for each input

8. *ORDERED PAIRS* Don’t forget that a relation has brackets { } on the outsides and parenthesis ( ) around each set.
Function:
Non-Function:

9. Ordered Pairs: “x” is the input, and “y” is the output
{(-1, 1), (-2, -3), (-3, 3)} {(4, 2), (4, 5), (6, 8), (10,8)}
Functions have EXACTLY ONE output for each input

10. Ordered Pairs: “x” is the input, and “y” is the output
{(-1, 1), (-2, -3), (-3, 3)} {(4, 2), (4, 5), (6, 8), (10,8)}
FUNCTION – none of the “x” values repeat
RELATION – there are two 4’s in the “x” value
Functions have EXACTLY ONE output for each input

11. Graphs: Vertical Line Test:
**If you draw a straight line down through your graph, and it hits only once, then the graph is a function. If it hits more than once, then the graph is not a function, but a relation.
Function:
Non-Function:

12. Graphs: Vertical Line Test:
**If you draw a straight line down through your graph, and it hits only once, then the graph is a function. If it hits more than once, then the graph is not a function, but a relation.

13. Vertical Line Test:
**If you draw a straight line down through your graph, and it hits only once, then the graph is a function. If it hits more than once, then the graph is not a function, but a relation.
Non - Function
Function
Function

14. Linear vs. Non Linear:

15. One output for each input Common difference / straight line
RELATIONS
(Sets of Data)
FUNCTION
One output for each input
LINEAR
Common difference / straight line
NON - LINEAR

16. Only functions are linear.
Linear or Non-Linear
Only functions are linear.
For a function to be linear, there has to be a common difference – this means to look at the outputs, and if you get the same solution when you subtract, you have a common difference.
Linear functions, when graphed, form a straight line.

17. Graph:
**It means formed by a line **These linear equations look like a line when graphed Linear Non-Linear

18. Table:
To determine if a table has a linear relationship, look for a common difference (SLOPE). x 1 2 3 4 y 6 9 12 x 4 5 6 7 y 16 25 36 49
CD:
CD:

19. Equation:
If you want to check if an equation is linear, use the check list: NO exponents x3 No variables being multiplied together 6xy No variables in denominator 𝟑𝐱 𝐲
3 checks = LINEAR

20. Is it Linear??
*When looking at a graph, if it makes a straight line, IT’S LINEAR. *When looking at a table, if there is a common difference, IT’S LINEAR. *When looking at an equation, if there are no exponents, no variables multiplied together, and no variables in the denominator, IT’S LINEAR.

21. Ticket Out The Door…
On your sticky note, write down if you think the following functions are LINEAR or NON - LINEAR

22. 2a + 3b = 4 y = 5x – 3xy y = 1 x A = s2 *No Exponents
*No variables being
multiplied together
*No variable in denominator

23. 2a + 3b = 4 LINEAR y = 5x – 3xy NON - LINEAR y = 1 x A = s2