Clarification on Functions
Math 8
C1 U2 K3
X1 Z2 A3
G1 B2 H3
M1 E2 D3
B3 U2 K7
A7 Z2 A9
G5 B4 H2
M6 A9 D1
A1 D2 E3
G1 B2 K3
C1 E2 H3
D1 J2 E3
Z6 T6 H9
L9 N6 W9
Q6 V9 Q9
V6 Q9 T6
Function Definition:
Each input (x) has one output (y)
Function
Not a Function
Input of 2 has two different outputs
Error 1: Each input has an output
Each person has an apple.
Does any person have more than 1?
Error 2: Each input has its own output
inputs can share the same output
Error 3: Only one input per output
Error 4: Each domain has one range
Vocabulary:
Domain is the group of inputs
Range is the group of outputs
inputs are
-1, 0 , 3, 6, and 14
Functions:
x | f(x) |
− 4 | 10 |
−1 | 2 |
6 | − 4 |
2 | 55 |
− 1 | 10 |
10 | 10 |
Is this a function? Explain
− 4
− 1
2
6
10
− 4
2
10
55
Inputs Outputs
Not a function! The input of −1 has two different outputs
Error 5: Stating it is a function because all the x’s are different.
or that there are no duplicates in the x/inputs
x | f(x) |
− 2 | 10 |
−10 | 20 |
6 | 35 |
23 | 55 |
− 2 | 10 |
6 | 35 |
Duplicates in the x values
can still be a function
if the outputs also match
Use the definition of Function
word-for-word to explain best
Function:
passes the Vertical Line Test --- Graph only!
Function
Not a Function
Functions
Is this a function? Explain
No! it fails the
Vertical Line Test
Is this a function? Explain
Yes it is a Function. There are duplicates in the domain, but each input has exactly ONE output
Is this a function? Explain
Not a function!
The input of 4 has
two different outputs
Not a function!
The input of −3 has
two different outputs
Is this a function? Explain
Not a function!
The input of 9 has
two different outputs
Function!
Each input has
exactly one output