Introduction to Functions
Math 8
Students love getting snacks from the vending machines
Programming a machine like this to
work properly is important
A1 A2 A3
B1 B2 B3
C1 C2 C3
D1 D2 D3
What selection would you need to make
to receive the specified item?
Oreos
Lays
KitKat
Takis
What item will you receive with the
specified selection?
D1
B3
A2
Is this vending machine programmed
to work properly?
C2
A3
B1
A1
Mint Mentos
Reese’s
Doritos
YES
C1 C2 C3
What selection would you need to make
to receive the specified item?
Oreos
M&Ms
Doritos
Takis
What item will you receive with the
specified selection?
C3
B3
D2
Is this vending machine programmed
to work properly?
A1 A2 A3
B1 B2 B3
D1 D2 D3
Famous
Amos
B2
A2
C2 or D3
A1 or A3 or C1 or D2
Fruit Mentos
Takis
YES
C3 D2 A1
A3 B2 B3
C3 D2 C3
D1 C3 B2
What selection would you need to make
to receive the specified item?
Mint Mentos
Reese’s
Tic Tacs
Takis
What item will you receive with the
specified selection?
A3
D2
C3
Is this vending machine programmed
to work properly?
D1
B3
C3 will not always
give the correct item
B2 will not always
give the correct item
KitKat
Unpredictable
Doritos or Oreos
NO
Unpredictable
Takis or Pretzels or
Cookies or
Fruit Mentos
D1 D2 D3
Is the vending machine
programmed to work
properly?
C4 C4 C4
C4 C4 C4
C4 C4 C4
C4 C4 C4
A1 A2 A3
B1 B2 B3
C1 C2 C3
It is fine for several buttons
to return the same item
It will NOT work for one button
to return a random item
CHAOS!
🤯
When a vending machine works properly
we could say that it is consistently doing its
The selection you make could be called
the input of the function
FUNCTION
The item you receive could be considered
the output of the function
It is important that each selection
made produces the correct item.
Vocabulary
A relation in which each input has exactly one output
Vocabulary
- a list of all inputs, the x-values,
in order from least to greatest
- duplicate values are only listed once
- use set notation
Vocabulary
- a list of all outputs, the y-values,
in order from least to greatest
- duplicate values are only listed once
- use set notation
State the domain and range and then determine if the following relations are functions
{ 2 , 3 , 4 , 8 }
{ 6 , 10 , 12 }
2
3
4
8
6
10
12
(x , y)
Domain:
Range:
This is a function because each input
has exactly one output.
x y
Domain:
Range:
{ 6 , 9 , 10 }
{ 12 , 18 , 27 , 40 }
6
9
10
12
18
27
40
This is NOT a function because the input of 6 has two different outputs.
State the domain and range and then determine if the following relations are functions
Domain:
Range:
{−3 , −2 , 1 , 2 }
{ −5 , − 2 , 3 , 4 }
This is NOT a function because the input of −3 has two different outputs.
(−3, 4)
(−2, 3)
(2 , 3)
(−3,−2)
(1,−5)
State the domain and range and then determine if the following relations are functions
Vocabulary
-if a vertical line passing across a graph only touches one point at a time it is a function
Use the Vertical Line Test on the previous graph
This is NOT a function because it fails the Vertical Line Test at the input of −3
Use the Vertical Line Test to determine if the following relations are functions
This is a function because it passes the Vertical Line Test
You have permission to abbreviate this to VLT
Use the Vertical Line Test to determine if the following relations are functions
This is NOT a function because it does not passes the Vertical Line Test
There are two inputs (5 and 6) that have multiple outputs
Determine if the following relations are functions.
If not, explain.
This is a Function because each input has exactly one output
Determine if the following relations are functions.
If not, explain.
This is a Not a Function because the input of 5 has two different outputs
Hint: Pay close attention to duplicates in the inputs.
If there are no duplicate inputs it is guaranteed to be a function.
Must use the definition of function as explanation
This has duplicate inputs
BUT it is still a Function because each duplicate input is paired with the same output
Determine if the following relations are functions.
If not, explain.
This is a Function because each input has exactly one output
Determine if the following relations are functions.
If not, explain.
This is a Not a Function it fails the Vertical Line Test multiple places
Is this a function? Create a mapping. �What type of situation would this set of ordered pairs look like?
−14
−13
−8
5
8
2
This is a Function because each input has exactly one output
Is this a function? Create a mapping. �What type of situation would this set of ordered pairs look like?
4
−20
−11
0
1
1362
This is Not a Function because the input 4 has 5 different outputs
Plotting these points on a graph would fail the Vertical Line Test