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FUN with Functions!
Lesson Study Group B
February 2012
Objectives
• I will be able to use a function table to write
an equation.
• I will be able to use the equation to complete
the missing values in the function table.
Algebra and FUNCTIONS 1.5
Prior Knowledge
Finding Patterns
• Find a pattern between the yellow column
and the blue column.
4
1
7
9
3
6
4
6
0
3
The pattern is subtract 3
Prior Knowledge
Finding Patterns
• Find a pattern between the yellow row and
the blue row.
The pattern is multiply by 3
3
5
0
9
12
9
15
0
27
36
Prior Knowledge
Finding Patterns
• Find a pattern between the yellow column
and the blue column.
16
4
4
8
36
24
1
2
9
6
The pattern is divide by 4
Prior Knowledge
Finding Patterns
• Find a pattern between the yellow row and
the blue row.
The pattern is add 2
3
5
7
0
1
5
7
9
2
3
What is a Function?
x 8
y
+4
12
A function is a rule, that for every value of x
(input) gives exactly one value of y (output).
What is a Function?
x 7
y
+4
11
A function is a rule, that for every value of x
(input) gives exactly one value of y (output).
Functions
In the incomplete equation
+ 5 = ___
is the input (x)
+ 5 is the rule
x+5=y
y=x+5
_____ is the output (y)
What is a Function Table?
x
y
4a
8a
a
36
a
24
1a
2a
9a
6a
• A function table is a
way of organizing
values.
• Now you can find a
pattern between an x
value and a y value to
write an equation.
Connecting a Function to its Table
Let’s imagine this equation
The input is
a number
going in.
+ 5 = ___
+ 5 is the rule
x (input)
y (output)
The output is
the result of
applying the
rule ( + 5)
Steps for Writing an Equation
• Step 1: Find a pattern
• Step 2: Identify the rule
• Step 3: Write an equation by adding x and y
to the rule.
Writing an equation
x
y
5
0
9
12
15
0
27
36
The rule is…
·3
= ___
3x = y
y = 3x
Writing an equation
x
y
7
9
3
6
4
6
0
3
The rule is…
-3 =
___
y=x-3
Writing an equation
x
5
7
0
1
y
7
9
2
3
The rule is…
y=x+2
+2
= ___
Writing an equation
x
25
35
10
5
y
5
7
2
1
The rule is…
y=x÷5
x
y 
5
÷ 5 = ___
Steps for Writing an Equation
Steps to Completing a Function Table
• Step 1: Find a pattern
• Step 2: Identify the rule
• Step 3: Write an equation by adding x and y to
the rule.
• Step 4: Use the x value to calculate
the y value.
Function Tables
The rule is:
x
y
+ 5 = ___
x
y
5
7
10
13
15
17
10
12
15
18
20
22
Function Tables
The rule is:
x
y
· 3 = ___
x
y
6
4
5
7
3
10
18
12
15
21
9
30
Function Tables
Equation
x–6=y
y=x-6
x
y
18
10
20
9
16
6
12
4
14
3
10
0
Function Tables
Equation
x–4=y
y=x-4
x
6
9
11
20
15
40
y
2
5
7
16
11
36
Function Tables
Equation
x÷4=y
y=x÷4
x
y
20
8
4
24
12
28
5
2
1
6
3
7
Function Tables
Equation
x ·6 = y
y=x·6
x
y
3
5
0
9
6
7
18
30
0
54
36
42
Function Tables
x+9=y
Equation
y = x +9
x
2
22
13
8
7
0
y
11
31
22
17
16
9
Function Tables
Equation
x ÷8 = y
y=x÷8
x
y
32
24
16
88
56
48
4
3
2
11
7
6
CST Released Question
x
y
9
2
4
11
81
18
36
99
Which equation could
have been used to create
this function table?
a)
b)
c)
d)
y=x+9
y=x–9
y = 9x
x
y= 9
Justify your answer
Word Problem
Number of
Family
Members
1
2
5
9
Total Cost for
Tickets
$17
$34
$85
Choose the number to
complete the function
table to find how much 9
tickets will cost.
a) $8
b) $102
c) $136
d) $153
Justify your answer
Which table represents values of x and y
such that y = x + 7?
A.
B.
x
y
1
C.
x
y
8
2
9
4
10
3
11
x
Y
x
y
9
2
4
11
6
1
2
9
D.
Justify your answer
Objectives
• I will be able to use a function table to write
an equation.
• I will be able to use the equation to complete
the missing values in the function table.
Ticket Out the Door!
QUIZ
Complete quiz from today’s
lesson with the following
information:
 Rule
 Equation
 Explanation
 Complete function table
You Rule!
Create your own function table
with the following information:
 Rule
 Equation
 Completed Table:
 must have an x and a y
 include at least 4 rows of
numbers
 Write a real life situation to go
with your table
Guess My Rule!
Partner B pulls a card
Input
Output
Partner A Partner B
Partner A pulls a card
Input
Output
Partner A Partner B