Question

A function has the rule “halve the input, then subtract 6.”
Using x to represent the input, complete the diagram with an expression for this rule. What expression represents “halve the input, then subtract 6?”
x
Input Output Arrow
Input Output Arrow
y

Answer 1

To represent the function that "halves the input, then subtracts 6," we can break down the process step by step:

1. **Halve the input (x)**:
This can be represented mathematically as \(\frac{x}{2}\).

2. **Subtract 6 from the result of halving**:
After halving the input, we subtract 6 from that result. Therefore, we take \(\frac{x}{2}\) and subtract 6, which gives us the expression:
\[
\frac{x}{2} - 6
\]

Now, we can represent this in the context of your diagram.

- Input: \(x\)
- Process: "halve the input, then subtract 6"
- Output (y): \(\frac{x}{2} - 6\)

Thus, the completed expression for the rule in the diagram would be:
- Output: \(y = \frac{x}{2} - 6\)