In simpler terms we might say for every x value there is only one y

G.CO.A.2 STUDENT NOTES & PRACTICE WS #2 – geometrycommoncore.com
1
Review of Functions
A correspondence between two sets A and B is a FUNCTION of A to B
IF AND ONLY IF each member of A corresponds to one and only one member of B.
In simpler terms we might say for every x value there is only one y value.
We sometimes diagram these types of relationships with DOMAIN (x values) and a RANGE (y values)
boundaries.
This is a function.
Each value in set A (Domain)
has exactly one value in set B (Range).
Each value in set A (Domain)
has exactly one value in set B (Range).
This is a function.
Notice that an x value can have the same y value as
another x value. Each x value still only has one y value.
This is a NOT function.
A member of Set A (Domain)
has two values in set B (Range),
thus it is NOT A FUNCTION.
Each value in set A (Domain)
has exactly one value in set B (Range).
This is a function.
Notice that an x value can have the same y value as
another x value. Each x value still only has one y value.



A quick way to determine if it is not a function is if one of the x values has more than one y value.
Notice that the domain and range could have the same number of elements or that the range could
have fewer elements and still be a function.
If the range had more elements than the domain then it will not be a function.
NYTS (Now You Try Some)
1.
2.
3.
Is this a function?
Is this a function?
Is this a function?
YES
YES
YES
OR
NO
OR
NO
OR
NO
G.CO.A.2 STUDENT NOTES & PRACTICE WS #2 – geometrycommoncore.com
2
WHAT IS A MAPPING?
A correspondence between the pre-image and image is a MAPPING
IF AND ONLY IF each member of the pre-image corresponds to one and only one member of the image.
A mapping works exactly like a function….


The pre-image and the image could have the same number of points or the image could have fewer
points.
If an image has more points than the pre-image then it will not be a mapping.
If the pre-image is KLM,
K maps to N
L maps to O
M maps to P
O
L
This is a mapping.
N
M
P
K
L
If the pre-image is KLM,
M maps to R
K maps to Q
L maps to Q
Q
This is a mapping.
K
M
R
L
If the pre-image is KLM,
K maps to S
L maps to T
M maps to U
M maps to V
T
This is NOT a mapping.
K
S
U
M
V
If the pre-image is KLM,
K maps to T
L maps to T
M maps to T
L
This is a mapping.
K
T
M
NYTS (Now You Try Some)
C
H
D
D
E
H
E
F
F
5.
Is this a mapping?
Pre-Image ABCDEF to Image GHI
YES
OR
NO
M
A
B
I
G
L
B
A
F
E
I
G
4.
C
B
G
C
J
K
A
Is this a mapping?
Pre-Image ABCDEF to Image GHIJKLM
YES
OR
NO
D
6.
H
Is this a mapping?
Pre-Image ABCD to Image EFGH
YES
OR
NO
G.CO.A.2 STUDENT NOTES & PRACTICE WS #2 – geometrycommoncore.com
3
Not all mappings are useful…… we don’t want to start with a triangle and end up with a segment or a point
after we map them. We want to study the mappings that preserve the number of points between the preimage and image. In Algebra when there is exactly the same number of elements in the domain as there is in
the range it is called a ONE TO ONE FUNCTION. In geometry, when you have the same number of points in
the pre-image as in the image, it is called a TRANSFORMATION.
ONE TO ONE FUNCTION
NOT ONE TO ONE FUNCTION
A TRANSFORMATION
L
M
K
N
NOT A TRANSFORMATION
L
M
N
K
L'
M'
K'
N'
T
U
S
Transformations and One to One Correspondence Functions
A transformation is a one to one correspondence between the points of the pre-image and the points of the
image. We will only be studying transformations. A transformation guarantees that if our pre-image has
three points, then our image will also have three points.
NYTS (Now You Try Some)
E
H
B
G
C
I
G
E
F
F
A
8.
Is this a transformation?
Pre-Image ABCDEF to Image GHI
OR
NO
A
J
K
A
Is this a transformation?
Pre-Image ABCDEF to Image GHIJKLM
YES
OR
D
9.
H
Is this a transformation?
Pre-Image ABCD to Image EFGH
NO
YES
OR
NO
A transformation must have a pre-image and an image
WITH THE EXACT SAME NUMBER OF POINTS.
2. No, 2 y values for a single x
6. Yes
7. No
3. Yes
4. Yes
8. No, more points in the image
9. Yes
YES
M
B
I
G
L
B
7.
F
E
Answers:
1. Yes
5. No, more points in the image
C
C
H
D
D