Name __________________________________________________
Block __________________ Unit 6
Relations, Functions
Relation: any set of ordered pairs
Table
x
1
-2
4
-3
{ (1,3), (–2, 0), (4,2), (–3, –4)}
Mapping
y
3
0
2
-4
1
-2
4
-3
3
0
2
-4
Graph
x
y
Domain- The set of ALL x-values
Range- The set of ALL y-values
Input- the x-coordinate (x-value) of the point
Output- the y-coordinate (x-value) of the point
Independent variable can be assigned any
Dependent variable has its value determined by the
permissible value, causes a change in another variable
other variable
X
f(x) is the output, after function rule f was applied
to input x
_ Input __
__ Domain ____
x
{ (1,3), (–2, 0)}
______ Range __
y
Input
Output
__ Output _____
Output
Domain _
Domain
Input
_ Range
Input, independent variable
y = 2x - 1
Output, dependent variable
Range
Identify the domain and the range of the relation:
5)
1) (2, 5), (5, 11), (7, 15), (8, 17)
2) (-2, -1), (-1, -3), (0, -5), (1, -7)
Domain __{2, 5, 7, 8}____
Domain ___{–2, –1, 0, 1}_________
Range ___5, 11, 15, 17, ___________
Range ____{–1, –3, –5, –7}___________
3) (12, 1), (10, 3), (8, 5), (6, 7)
4) (-4, -2), (-6, -3), (-8, -4), (-10, -5)
Domain ___________________________
Domain ___________________________
Range ____________________________
Range ____________________________
x
5
6
7
8
9
y
1
2
3
4
5
x
-2
-1
0
1
2
6)
y
8
8
8
8
8
7)
x
-5
-7
-9
-11
-13
y
-1
-2
-3
-4
-5
Domain: {5, 6, 7, 8, 9}
Domain: {–2, –1, 0, 1, 2}
Domain: _______________
Range: {1, 2, 3, 4, 5}
Range: __{8}____
Range: ________________
Relation
Function
f(x) = x + 1
NOT a function
Definition
A relation
where each
repeated input
(if exists)
provides the
same output
A relation
where repeated
input provides
different,
unpredictable
outputs
Table
Graph
Mapping
x
–2
0
2
2
f(x), y
–1
1
3
3
-2
0
2
-1
x
–2
0
2
2
y
–1
1
3
–2
-2
0
2
-1
1
3
-2
Ordered Pairs
{(–2,–1), (0, 1),
(2, 3), (2, 3)}
1
3
{(–2,–1), (0, 1),
(2, 3), (2, –2)}
Is this a function? #1. Do we have repeated inputs? (No- it’s a function; Yes- see #2);
#2. Do repeated inputs have the same outputs? (the same- function;
different- just a relation)
Is the relation a function? Yes or No?
x
5
-6
5
-2
-1
y
-5
9
3
8
7
7) ___No___
x
-2
-1
0
-1
-5
x
1
0
2
3
4
y
0
4
8
6
5
8) ___ No ____
x
-9
7
-5
7
-6
y
5
8
0
4
6
9) __Yes__
y
9
8
5
8
6
10) __ Yes ____
11) (-5, -2), (-4, -3), (-5, -4), (3, 2)
12) (2, 4), (-2, 4), (0, 1), (-8, 4)
Is this relation a function? _ No _
Is this relation a function? _ Yes __
Vertical Line Test – another way to determine whether the relation is a function.
11) __ Yes __
12) __ No ____
13) ___ No __
______________ – a set of ordered pairs (x, y)
______________– collection of all the x-values of a function
______________ – the x-coordinates of the relation (ordered pairs)
______________– collection of all the y-values of a function
______________ - the y-coordinates of the relation (ordered pairs)
14) ___ Yes ___