functions: functions have exactly one output for each input – **each input can match up to only...
DESCRIPTION
*MAPPING* Function: Non-Function:TRANSCRIPT
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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
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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.
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*MAPPING*
Function:
Non-Function:
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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
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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
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*TABLES*Function:
Non-Function:
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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
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*ORDERED PAIRS*Don’t forget that a relation has brackets { } on the outsides and parenthesis ( ) around
each set.
Function:
Non-Function:
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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
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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
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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:
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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.
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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
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Linear vs. Non
Linear:
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RELATIONS(Sets of Data)
FUNCTIONOne output for each input
LINEARCommon difference /
straight lineNON - LINEAR
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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.
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Graph:**It means formed by a line**These linear equations look like a line when
graphed
Linear Non-Linear
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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:
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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
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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.
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Ticket Out The Door…On your sticky note, write down if you think the following functions are
LINEAR or
NON - LINEAR
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2a + 3b = 4
y = 5x – 3xy
y = 1 x
A = s2
*No Exponents*No variables being multiplied together*No variable in denominator
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2a + 3b = 4LINEAR
y = 5x – 3xyNON - LINEAR
y = 1 x
NON - LINEAR
A = s2
NON - LINEAR