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```1. Pick up your Builder and Weekly.
2. Turn in Builder to tray at the door.
3. Write your weekly agenda in your
planner.
4. Please complete the NEXT two
How would you use your calculator
to solve 52?
Input
Press:
5
Output
x2
25
The number you entered is the input
number (or x-value on a graph).
The result is the output number (or yvalue on a graph).
The x2 key illustrates the idea of a
function.
A function is a relation that gives a single
output number for every valid input number.
A relation is a rule that produces one or more
output numbers for every valid input number.
There are many ways to represent relations:
Graph
Equation
Table of values
A set of ordered pairs
Mapping
These are all ways of
showing a relationship
between two variables.
A function is a rule that gives a single output number
for every valid input number.
To help remember & understand the definition:
Think of your input number, usually your
x-coordinate, as a letter.
Think of your output number, usually your
y-coordinate, as a mailbox.
A function is a rule that gives a single output number
for every valid input number.
Input number
Output number
Can you have one letter going to two different mail boxes?
Not a FUNCTION
A function is a rule that gives a single output number
for every valid input number.
Input number
Output number
Can you have two different letters going to one mail box?
Is this a function?
x
1
2
3
4
y
5
6
7
Function
x
1
2
3
4
y
5
6
7
6
Is this a function?
Not a Function!
x
1
y
5
6
2
7
x
1
2
1
1
y
5
6
7
6
Is this a function?
x
y
1
5
2
6
3
8
11
Not a function!
x
1
2
2
3
y
5
6
11
8
In words:
Double the number and add 3
As an equation:
y = 2x + 3
As a table of values:
x y
-2 -1
-1 1
0 3
1 5
These all
represent the
SAME function!
As a set of ordered pairs:
(-2, -1) (-1,1) (0,3) (1, 5) (2, 7) (3, 9)
Example 1
{(0, 5), (1, 4), (2, 3), (3, 2), (4, 1), (5, 0)}
•Is this a function?
•Hint: Look only at the x-coordinates
YES
Example 2
{(–1, 7), (1, 0), (2, 3), (0, 8), (0, 5), (–2, 1)}
•Is this a function?
•Hint: Look only at the x-coordinates
NO
Example 3
Which mapping represents a function?
Choice One
3
1
0
–1
2
3
Choice Two
2
–1
3
Choice 1
2
3
–2
0
Example 4
Which mapping represents a function?
A.
B.
B
Vertical Line Test
•Vertical Line Test: a relation is a function
if a vertical line drawn through its graph,
passes through only one point.
AKA: “The Pencil Test”
Take a pencil and move it from left to right
(–x to x); if it crosses more than one point,
it is not a function
Vertical Line Test
Would this
graph be a
function?
YES
Vertical Line Test
Would this
graph be a
function?
NO
A FUNCTION is a relation in which each first value is paired with one and ONLY ONE second value.
Relation (a set of ordered pairs)
x y
( 1 , 2 ) Decide whether the relation
( 1 , -1 )
(4 , 6)
-3
-1
0
-3
1
y
-7
-3
2
-5
4
x
y
Why or why not?
____________________
-2
1
0
3
____________________
2
5
Why or why not?
_______________________
____________________
4
7
_______________________
6
9
_______________________
(6 , 8)
Mapping
11
13
17
-9
x
Yes or No
is a function.
(3 , 4)
Input-Output
Tables
8
12
16
Decide whether
the relation is a
function. Yes or
No
Why or why not?
______________
______________
______________
______________
Decide whether the relation is a
function.
Yes or No
Vertical Line Test for Functions: a VERTICAL line crosses only
one point on the graph
Decide whether the
relation is a
function. Yes or No
Why or why not?
_______________
_______________
_______________
_______________
Identifying Functions
Name: ________________
Part A: Determining Function with Tables and Mappings
Determine if each relation below is a function.
1.
2.
Function: Y N
Function: Y
N
3.
Function: Y
N
```