functions: functions have exactly one output for each input – **each input can match up to only...

Functions:Functions have EXACTLY ONE

output for each input –**Each input can match up to only one output

Examples:ATM Vending Machine Key – LockGas Station Calculator Remote ControlPencil Sharpener Phone KeyboardCD Player Oven

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.

*MAPPING*

Function:

Non-Function:

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

0

4

8

12

15

Functions have EXACTLY ONE output for each input

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

0

4

8

12

15

Functions have EXACTLY ONE output for each input

Not a Function: Tia and Tom have 2 outputs each

Not a Function: 18 has 2 outputs

Function: each input has only 1 output

*TABLES*Function:

Non-Function:

Tables:

x y1 32 22 103 4

x y2 83 95 104 11

“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).

Functions have EXACTLY ONE output for each input

*ORDERED PAIRS*Don’t forget that a relation has brackets { } on the outsides and parenthesis ( ) around

each set.

Function:

Non-Function:

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

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

FUNCTION – none of the “x” values repeat

RELATION – there are two 4’s in the “x” value

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:

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.

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.

FunctionNon - Function

Function

Linear vs. Non

Linear:

RELATIONS(Sets of Data)

FUNCTIONOne output for each input

LINEARCommon difference /

straight lineNON - LINEAR

Linear or Non-LinearOnly 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.

Graph:**It means formed by a line**These linear equations look like a line when

graphed

Linear Non-Linear

Table:

x 1 2 3 4 y 3 6 9 12

To determine if a table has a linear relationship, look for a common difference (SLOPE).

x 4 5 6 7 y 16 25 36 49

CD: CD:

Equation:If you want to check if an equation is linear, use

the check list:

NO exponentsx3

No variables being multiplied together6xy

No variables in denominator

3 checks = LINEAR

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.

Ticket Out The Door…On your sticky note, write down if you think the following functions are

LINEAR or

NON - LINEAR

2a + 3b = 4

y = 5x – 3xy

y = 1 x

A = s2

*No Exponents*No variables being multiplied together*No variable in denominator

2a + 3b = 4LINEAR

y = 5x – 3xyNON - LINEAR

y = 1 x

NON - LINEAR

A = s2

NON - LINEAR