Function Machines Textbook Exercise - Corbettmaths - Free Printable

Let's solve each part of the Function Machines problems step by step.

---

Question 1: Function Machine – "Add 9"

The function machine takes an input, adds 9 to it, and gives the output.

So the rule is:
> Output = Input + 9

---

#### (a) Output when input is 12
$$
\text{Output} = 12 + 9 = \boxed{21}
$$

---

#### (b) Output when input is 35
$$
\text{Output} = 35 + 9 = \boxed{44}
$$

---

#### (c) Input when output is 14

We know:
$$
\text{Output} = \text{Input} + 9
$$
So,
$$
14 = \text{Input} + 9
$$
Subtract 9 from both sides:
$$
\text{Input} = 14 - 9 = \boxed{5}
$$

---

#### (d) Input when output is 10.5

$$
10.5 = \text{Input} + 9
$$
$$
\text{Input} = 10.5 - 9 = \boxed{1.5}
$$

---

✔ Summary for Question 1:

- (a) 21
- (b) 44
- (c) 5
- (d) 1.5

---

Question 2: Function Machine – "Divide by 4"

The rule is:
> Output = Input ÷ 4

---

#### (a) Output when input is 40
$$
\text{Output} = 40 ÷ 4 = \boxed{10}
$$

---

#### (b) Output when input is 22
$$
\text{Output} = 22 ÷ 4 = \boxed{5.5}
$$

---

✔ Summary for Question 2:

- (a) 10
- (b) 5.5

---

🔍 Explanation:

Function machines help visualize how inputs are transformed into outputs using a specific operation.

- For forward calculations (input → output), just apply the operation.
- For reverse calculations (output → input), do the inverse operation:
- If the machine says "Add 9", reverse is "Subtract 9".
- If it says "Divide by 4", reverse is "Multiply by 4".

This concept is foundational in algebra and helps build understanding of equations and inverses.

Let me know if you'd like these explained with diagrams or real-life analogies!