functions: functions have exactly one output for each input – **each input can match up to only...
DESCRIPTION
*MAPPING* Function: Non-Function:TRANSCRIPT
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