Math Skill: Function Tables 2
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Function Tables 2

This topic continues the topic of function tables.
To review the basics of function tables, see here.

Example 1: Apply the rule

Use the given rule to fill in the missing values.
y = x ÷ 4
Input (x)Output (y)
24
4
8
36

Find the missing y values, substitute the input values for x in the rule ( y = x ÷ 4).

24   →
 24 ÷ 4
→   6
4   →
 4 ÷ 4
→   1
36   →
 36 ÷ 4
→   9

 To find the missing x value, solve for y. y = x ÷ 4 8 = x ÷ 4 8 × 4 = x ÷ 4 × 4 32 = x
y = x ÷ 4
Input (x)Output (y)
24
4
2
36

Example 2: Word problem

Fill in the missing values and find the rule that applies to the table. Write the rule in the format "y = ".
Maria has 5 more cookies than Jeremy.
Rule:
9
7
8
1

1.   Find the rule

Translate the sentence into an algebraic expression.
 Maria has 5 more cookies than Jeremy Number of cookies Maria has is 5 more than the number of cookies Jeremy has y = + 5 x
So the rule is y = x + 5.
2.   Apply the rule
To apply the rule ( y = x + 5), substitute the input values for x in the rule.
9   →
 9 + 5
→   14
7   →
 7 + 5
→   12
8   →
 8 + 5
→   13
1   →
 1 + 5
→   6
Rule:
9
7
8
1

Example 3: Word problem

Fill in the missing values and find the rule that applies to the table. Write the rule in the format "y = ".
Octagons have 8 sides.
Rule:
Number of octagons (x)Number of sides (y)
8
3
6
2

1.   Find the rule

Translate the sentence into an algebraic expression.
This is a rate problem where the rate is 8 sides per octagon.
So,
 number of sides = sides per octagon × number of octagons y = 8 × x
So the rule is y = 8x.
2.   Apply the rule
To apply the rule ( y = 8x), substitute the input values for x in the rule.
8   →
 8(8)
→   64
3   →
 8(3)
→   24
6   →
 8(6)
→   48
2   →
 8(2)
→   16
Rule:
Number of octagons (x)Number of sides (y)
8
3
6
2

### Complexity=1, Mode=givenRule

Use the given rule to fill in the missing values.
1.
y = x + 9
Input (x)Output (y)
14
2
4
3
2.
y = x - 2
Input (x)Output (y)
4
12
6
1

### Complexity=2, Mode=givenRule

Use the given rule to fill in the missing values.
1.
y = x ÷ 7
Input (x)Output (y)
49
2
63
56
2.
y = x ÷ 10
Input (x)Output (y)
10
20
80
70

### Complexity=1, Mode=word

Fill in the missing values and find the rule that applies to the table. Write the rule in the format "y = ".
1.   Tiffany has 7 fewer pens than John.
Rule:
# pens John has (x)# pens Tiffany has (y)
16
12
9
17
2.   Mary has 9 more pens than Pearl.
Rule:
# pens Pearl has (x)# pens Mary has (y)
9
3
1
10

### Complexity=2, Mode=word

Fill in the missing values and find the rule that applies to the table. Write the rule in the format "y = ".
1.   Each package contains 2 cookies.
Rule:
Number of packages (x)Number of cookies (y)
8
10
5
7
2.   Each package contains 3 cookies.
Rule:
Number of packages (x)Number of cookies (y)
2
1
4
9

### Complexity=3, Mode=givenRule

Use the given rule to fill in the missing values.
1.
y = 6x + 1
Input (x)Output (y)
5
1
4
3
2.
y = 3x + 6
Input (x)Output (y)
6
5
1
9

### Complexity=1, Mode=givenRule

Use the given rule to fill in the missing values.
1
y = x + 9
Input (x)Output (y)
14
2
4
3
Solution

Substitute numbers in for known x values.

x y = x + 9 y
2   y = x + 9   =   2 + 9   =   11   11
4   y = x + 9   =   4 + 9   =   13   13
3   y = x + 9   =   3 + 9   =   12   12

To find the unknown x value, take the known y value and subtract 9.
2
y = x - 2
Input (x)Output (y)
4
12
6
1
Solution

Substitute numbers in for known x values.

x y = x - 2 y
4   y = x - 2   =   4 - 2   =   2   2
12   y = x - 2   =   12 - 2   =   10   10
6   y = x - 2   =   6 - 2   =   4   4

To find the unknown x value, take the known y value and add 2.

### Complexity=2, Mode=givenRule

Use the given rule to fill in the missing values.
1
y = x ÷ 7
Input (x)Output (y)
49
2
63
56
Solution

Substitute numbers in for known x values.

x y = x ÷ 7 y
49   y = x ÷ 7   =   49 ÷ 7   =   7   7
63   y = x ÷ 7   =   63 ÷ 7   =   9   9
56   y = x ÷ 7   =   56 ÷ 7   =   8   8

To find the unknown x value, take the known y value and multiply by 7.
2
y = x ÷ 10
Input (x)Output (y)
10
20
80
70
Solution

Substitute numbers in for known x values.

x y = x ÷ 10 y
20   y = x ÷ 10   =   20 ÷ 10   =   2   2
80   y = x ÷ 10   =   80 ÷ 10   =   8   8
70   y = x ÷ 10   =   70 ÷ 10   =   7   7

To find the unknown x value, take the known y value and multiply by 10.

### Complexity=1, Mode=word

Fill in the missing values and find the rule that applies to the table. Write the rule in the format "y = ".
1Tiffany has 7 fewer pens than John.
Rule:
# pens John has (x)# pens Tiffany has (y)
16
12
9
17
Solution
"Tiffany has 7 fewer pens than John." means
 Number of pens Tiffany has is 7 fewer than the number of pens John has y = - 7 x

So you get, y = x - 7
2Mary has 9 more pens than Pearl.
Rule:
# pens Pearl has (x)# pens Mary has (y)
9
3
1
10
Solution
"Mary has 9 more pens than Pearl." means
 Number of pens Mary has is 9 more than the number of pens Pearl has y = + 9 x

So you get, y = x + 9

### Complexity=2, Mode=word

Fill in the missing values and find the rule that applies to the table. Write the rule in the format "y = ".
Rule:
Number of packages (x)Number of cookies (y)
8
10
5
7
Solution
"Each package contains 2 cookies." means that there are 2 cookies per package.
For the number of cookies, multiply by the rate (cookies per package).
 number of cookies = cookies per package × number of packages y = 2 × x

So you get, y = 2x
Rule:
Number of packages (x)Number of cookies (y)
2
1
4
9
Solution
"Each package contains 3 cookies." means that there are 3 cookies per package.
For the number of cookies, multiply by the rate (cookies per package).
 number of cookies = cookies per package × number of packages y = 3 × x

So you get, y = 3x

### Complexity=3, Mode=givenRule

Use the given rule to fill in the missing values.
1
y = 6x + 1
Input (x)Output (y)
5
1
4
3
Solution

Substitute numbers in for known x values.

x y = 6x + 1 y
5   y = 6x + 1   =   6(5) + 1   =   31   31
1   y = 6x + 1   =   6(1) + 1   =   7   7
4   y = 6x + 1   =   6(4) + 1   =   25   25
3   y = 6x + 1   =   6(3) + 1   =   19   19
2
y = 3x + 6
Input (x)Output (y)
6
5
1
9
Solution

Substitute numbers in for known x values.

x y = 3x + 6 y
6   y = 3x + 6   =   3(6) + 6   =   24   24
5   y = 3x + 6   =   3(5) + 6   =   21   21
1   y = 3x + 6   =   3(1) + 6   =   9   9
9   y = 3x + 6   =   3(9) + 6   =   33   33