do now find the domain & range:. answers to homework 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12
TRANSCRIPT
Do NowFind the domain & range:
Answers to Homework
1.
2.
3.
4.
: ,
: ,
D
R
: ,
: ,
D
R
: ,
: 2,
D
R
: 5,1
: 4,2
D
R
: ,
: , 4
D
R
: , 1 1,2 2,
: ,
D
R
: ,
: ,
D
R
: , 4 4,
: , 2 2,
D
R
: ,
: , 2
D
R
: 4,
: , 3
D
R
: 5, 3
: 4,0
D
R
: ,
: 3,1
D
R
5.
6.
7.
8.
9.
10.
11.
12.
HomeworkNeed help?
Look in section 2.1 – Relations & Functions in your textbook
Worksheet: Functions WS
Unit 3: Domain & RangeDay 6: Relations & Functions
RelationsWhat is a relation?
A set of pairs of x – values and y – values
• State the relationRelation: (-5, 4), (-2, -5), (3, 0), (3, 8)
•State the domain of the relation in interval notation Domain: [-5] [-2] [3]
•State the range of the relation in interval notationRange: [-5] [0] [4] [8]
RelationsDescribing relations using a mapping diagramRelation: (-5, 4), (-2, -5), (3, 0), (3, 8)Domain: [-5] [-2] [3] Range: [-5] [0] [4] [8]
DOMAIN
RANGE#1: Create a column for domain and one for range#2: Add domain and range values-5
-23
-5048
#3: Draw arrows to show how each element in the domain pairs up with the elements in the range.
HOW TO CREATE A MAPPING DIAGRAM
RelationsGiven the relation below, state the domain and
range and create a mapping diagram.Relation: (6,-6), (7,-7), (3,-3), (5,-7)Domain: [3] [5] [6] [7]Range: [-7] [-6] [-3]DOMAIN
RANGE
3567
-7-6-3
FunctionsWhat is a function?
A relation where one element in the domain is paired with exactly one element in the range.
DOMAIN
RANGE
-5048
-5-23
Not a function because 3 in the domain is paired
with 0 and 8 in the range.
DOMAIN
RANGE
-504
-4038
Is a function because each element of the domain leads to one
element in the range.
Functions …another way to think about functions…
Function as a machine where a number goes in and are
manipulated (add, subtract, etc.) to turn into something
else.
Numbers that go in are the domain (x – values).
Numbers that come out are the range (y – values).
Every time you put a # into the
machine, the machine has to output only one
#.
Functions
This is not a function because when 12 is put into the machine, 12 or 5 is the output.
DOMAIN
RANGE
-251012
-71012
DOMAIN
RANGE
-8
-4038
This is a function because each element in the domain is paired to one element in range.
Determine if the relation is a function
DOMAIN
RANGE
-31510
-2179
DOMAIN
RANGE
114800
-7-4611
This is a function because when every number goes into the machine, you know exactly what the output will be.
This is a function because when every number goes into the machine, you know exactly what the output will be.
Determine if the relation is a function
X Y
-2 5
1 10
7 1
9 -3
X Y
-7 800
-4 1
6 14
11 14
The relation is a function because each input leads to exactly one output.
The relation is a function because each input leads to exactly one output.
Determine if the table shows a functionx y
-11 -31
-2 -4
0 2
7 23
x y
2 5
4 8
6 13
2 15
The relation is a function because each input leads to exactly one output.
The relation is not a function because 2 leads to outputs 5 and 15.
Did you meet today’s objective?What is a relation?What makes a relation a function?