Function Tables | Interactive Worksheet - Free Printable

To solve the problem, we need to determine the pattern in each input-output table and use it to calculate the missing numbers. Let's analyze each table step by step.

---

Table 1:

| IN | OUT |
|----|-----|
| 3 | 5 |
| 4 | 6 |
| 5 | |
| 7 | 9 |
| 9 | 11 |
| 10 | |

#### Pattern:
- Observe the relationship between "IN" and "OUT":
- \( 3 \rightarrow 5 \): \( 3 + 2 = 5 \)
- \( 4 \rightarrow 6 \): \( 4 + 2 = 6 \)
- \( 7 \rightarrow 9 \): \( 7 + 2 = 9 \)
- \( 9 \rightarrow 11 \): \( 9 + 2 = 11 \)

The pattern is: OUT = IN + 2.

#### Missing Values:
- For \( \text{IN} = 5 \):
\[
\text{OUT} = 5 + 2 = 7
\]
- For \( \text{IN} = 10 \):
\[
\text{OUT} = 10 + 2 = 12
\]

#### Completed Table:
| IN | OUT |
|----|-----|
| 3 | 5 |
| 4 | 6 |
| 5 | 7 |
| 7 | 9 |
| 9 | 11 |
| 10 | 12 |

---

Table 2:

| IN | OUT |
|----|-----|
| 3 | 4 |
| 4 | 5 |
| 5 | 9 |
| 7 | 13 |
| 9 | |
| 10 | 21 |

#### Pattern:
- Observe the relationship between "IN" and "OUT":
- \( 3 \rightarrow 4 \): \( 3 \times 1 + 1 = 4 \)
- \( 4 \rightarrow 5 \): \( 4 \times 1 + 1 = 5 \)
- \( 5 \rightarrow 9 \): \( 5 \times 2 - 1 = 9 \)
- \( 7 \rightarrow 13 \): \( 7 \times 2 - 1 = 13 \)
- \( 10 \rightarrow 21 \): \( 10 \times 2 + 1 = 21 \)

The pattern alternates:
- For odd "IN": \( \text{OUT} = \text{IN} \times 2 - 1 \)
- For even "IN": \( \text{OUT} = \text{IN} \times 1 + 1 \)

#### Missing Value:
- For \( \text{IN} = 9 \) (odd):
\[
\text{OUT} = 9 \times 2 - 1 = 18 - 1 = 17
\]

#### Completed Table:
| IN | OUT |
|----|-----|
| 3 | 4 |
| 4 | 5 |
| 5 | 9 |
| 7 | 13 |
| 9 | 17 |
| 10 | 21 |

---

Table 3:

| IN | OUT |
|----|-----|
| 2 | 3 |
| 3 | 6 |
| 5 | 10 |
| 7 | |
| 8 | 16 |
| 10 | |

#### Pattern:
- Observe the relationship between "IN" and "OUT":
- \( 2 \rightarrow 3 \): \( 2 \times 1 + 1 = 3 \)
- \( 3 \rightarrow 6 \): \( 3 \times 2 = 6 \)
- \( 5 \rightarrow 10 \): \( 5 \times 2 = 10 \)
- \( 8 \rightarrow 16 \): \( 8 \times 2 = 16 \)

The pattern is: OUT = IN × 2 for most values, except for \( \text{IN} = 2 \).

#### Missing Values:
- For \( \text{IN} = 7 \):
\[
\text{OUT} = 7 \times 2 = 14
\]
- For \( \text{IN} = 10 \):
\[
\text{OUT} = 10 \times 2 = 20
\]

#### Completed Table:
| IN | OUT |
|----|-----|
| 2 | 3 |
| 3 | 6 |
| 5 | 10 |
| 7 | 14 |
| 8 | 16 |
| 10 | 20 |

---

Table 4:

| IN | OUT |
|----|-----|
| 12 | 9 |
| 3 | 7 |
| 5 | 10 |
| 7 | 6 |
| 8 | 16 |
| 10 | 3 |

#### Pattern:
- This table does not follow a simple arithmetic pattern. Instead, it appears to be based on a different rule or sequence. However, without additional context, it's challenging to determine a consistent pattern. Let's assume it's a custom or irregular pattern and move on to the next tables.

---

Table 5:

| IN | OUT |
|----|-----|
| 4 | 1 |
| 5 | |
| 8 | 6 |
| 11 | 9 |
| 14 | 12 |
| 15 | |

#### Pattern:
- Observe the relationship between "IN" and "OUT":
- \( 4 \rightarrow 1 \): \( 4 - 3 = 1 \)
- \( 8 \rightarrow 6 \): \( 8 - 2 = 6 \)
- \( 11 \rightarrow 9 \): \( 11 - 2 = 9 \)
- \( 14 \rightarrow 12 \): \( 14 - 2 = 12 \)

The pattern seems to involve subtracting a number from "IN".

#### Missing Values:
- For \( \text{IN} = 5 \):
\[
\text{OUT} = 5 - 4 = 1
\]
- For \( \text{IN} = 15 \):
\[
\text{OUT} = 15 - 3 = 12
\]

#### Completed Table:
| IN | OUT |
|----|-----|
| 4 | 1 |
| 5 | 1 |
| 8 | 6 |
| 11 | 9 |
| 14 | 12 |
| 15 | 12 |

---

Table 6:

| IN | OUT |
|----|-----|
| 1 | 3 |
| 3 | 6 |
| 5 | 9 |
| 7 | 13 |
| 8 | 7 |
| 9 | 20 |

#### Pattern:
- Observe the relationship between "IN" and "OUT":
- \( 1 \rightarrow 3 \): \( 1 \times 3 = 3 \)
- \( 3 \rightarrow 6 \): \( 3 \times 2 = 6 \)
- \( 5 \rightarrow 9 \): \( 5 \times 1.8 \approx 9 \)
- \( 7 \rightarrow 13 \): \( 7 \times 1.857 \approx 13 \)
- \( 9 \rightarrow 20 \): \( 9 \times 2.222 \approx 20 \)

This table does not follow a simple consistent pattern. It may involve irregular multiplication factors.

---

Table 7:

| IN | OUT |
|----|-----|
| 0 | 3 |
| 2 | 8 |
| 5 | 15 |
| 3 | 18 |
| 4 | 16 |
| 6 | 21 |
| 9 | 27 |
| 7 | |

#### Pattern:
- Observe the relationship between "IN" and "OUT":
- \( 0 \rightarrow 3 \): \( 0 \times 3 + 3 = 3 \)
- \( 2 \rightarrow 8 \): \( 2 \times 3 + 2 = 8 \)
- \( 5 \rightarrow 15 \): \( 5 \times 3 = 15 \)
- \( 3 \rightarrow 18 \): \( 3 \times 6 = 18 \)
- \( 4 \rightarrow 16 \): \( 4 \times 4 = 16 \)
- \( 6 \rightarrow 21 \): \( 6 \times 3.5 = 21 \)
- \( 9 \rightarrow 27 \): \( 9 \times 3 = 27 \)

The pattern is inconsistent, so let's focus on the missing value for \( \text{IN} = 7 \).

#### Missing Value:
- Assume a linear pattern or trial-and-error:
- For \( \text{IN} = 7 \):
\[
\text{OUT} = 7 \times 3 = 21
\]

#### Completed Table:
| IN | OUT |
|----|-----|
| 0 | 3 |
| 2 | 8 |
| 5 | 15 |
| 3 | 18 |
| 4 | 16 |
| 6 | 21 |
| 9 | 27 |
| 7 | 21 |

---

Final Answer:

\[
\boxed{
\begin{array}{c}
\text{Table 1: } \begin{array}{c|c}
\text{IN} & \text{OUT} \\
\hline
5 & 7 \\
10 & 12 \\
\end{array} \\
\text{Table 2: } \begin{array}{c|c}
\text{IN} & \text{OUT} \\
\hline
9 & 17 \\
\end{array} \\
\text{Table 3: } \begin{array}{c|c}
\text{IN} & \text{OUT} \\
\hline
7 & 14 \\
10 & 20 \\
\end{array} \\
\text{Table 5: } \begin{array}{c|c}
\text{IN} & \text{OUT} \\
\hline
5 & 1 \\
15 & 12 \\
\end{array} \\
\text{Table 7: } \begin{array}{c|c}
\text{IN} & \text{OUT} \\
\hline
7 & 21 \\
\end{array}
\end{array}
}
\]