Identify the operations in the flow diagram.

The diagram shows an input value is first multiplied by $-4$, and then 3 is added to the result.

The relationship is: Multiply the input by $-4$, then add 3 to the result.

2.2.2

• For input $x = 0$:

• For input $x = 1$:

• For input $x = 4$:

• For input $x = 8$:

• For input $x = n$:

2.2.3

The original operations are: 1. Multiply by $-4$. 2. Add 3.
To reverse these, we perform the inverse operations in reverse order: 1. Subtract 3. 2. Divide by $-4$.

• Start with the output value: $-21$.
• Subtract 3 from the output: $-21 - 3 = -24$.
• Divide the result by $-4$: $-24 \div -4 = 6$.

The steps to calculate the input value for an output of $-21$ are:

1. Start with the output value, which is $-21$.
2. Subtract 3 from this value.
3. Divide the result by $-4$.