Guided Notes: Functions and Relations
Vocabulary
A relation can be represented by a set of _______________________________
The domain is the set of all ______________________________
The range is the set of all __________________________
The independent variable is the same as the ___-values and the ___________________
The dependent variable is the same as the ___-values and the ___________________
A relation is a function if for each ___-value there is exactly ______
___-value.
Each value in the domain of a function is called an _____________________, and
the corresponding value for the range is called an _______________________.
Examples: Identify the domain and range of each relation.
1. {(-2, 0), (0, 3), (4, -7), (-2, -1)
2.
Domain:
Range:
x
-4
-1
2
3
y
1
-5
8
1
Domain:
Range:
Examples: Determine whether the relation is a function. Explain why or why not.
3. {(-5, 0), (0, 1), (0, 4), (3, -7)}
4.
x
2
6
1
-1
y
1
3
8
3
5.
x
-1
0
3
3
y
-2
-3
0
1
When given a graph or picture of a relation and asked if it is a function the ______________
__________ ___________ is used. This test helps you to know a relation is a function by
looking to see if any ___________ line drawn does not intersect the graph at more than one
point. In other words on the graph each ___-value is paired with only one ___-value.
Examples: Determine if the graphs below represent functions or not by using the Vertical
Line Test.
y
6. 5
--
.
.
.
.
.
7. 5
x
5
--
y
8.
.. . .
.
x
5
9.
Mapping diagrams and tables can be used to determine if a relation is a function. In a mapping
diagram or table each ___-value will be paired with only one ___-value.
(A y-value may be paired with more than one x-value and the relation will still be a function.)
Examples: Determine whether the mapping diagram or table represents a function and circle
yes or no.
10.
function:
yes or no
13.
function:
yes or no
input
output
1
-4
3
0
-2
3
5
6
x
y
-6
1
3
8
2
7
11.
function:
yes or no
14.
function:
yes or no
x
y
-1
-2
3
4
8
5
12.
function:
yes or no
input
output
-4
-1
-1
2
0
7
5
15.
function:
yes or no
x
y
1
3
-2
-4
9
3
4
2
-5
3
input
output
-2
3
4
5
3
8
-2
4
It is a one to one function when every element of the range of the function corresponds to
exactly ______ element of the domain. y = f(x) is a function if it passes the __________ _____
________. It is a 1-1 function if it passes both the _________ ______ __________ and the
_____________ ______ __________ .
Examples: Determine whether the representations are one to one functions.
16.
17.
18.
x
y
1-1:
1-1:
1-1:
1
5
Yes or No
Yes or No
Yes or No
2
8
3
11
4
14
19.
x
y
20.
21.
1-1:
1
3
1-1:
1-1:
-2
-4
Yes or No
Yes or No
3
4
-5
3
Yes or No
22. Make a set of ordered pairs that represents a one to one function: