To create a mapping diagram for the rule "Subtract 3, and then multiply by 1/2" applied to the values \( x = -2, 0, 5 \), we will follow the steps outlined in the rule for each input value:
Step 1: Apply the Rule
-
For \( x = -2 \):
- Subtract 3: \[ -2 - 3 = -5 \]
- Multiply by \( 1/2 \): \[ -5 \times \frac{1}{2} = -\frac{5}{2} \text{ or } -2.5 \]
-
For \( x = 0 \):
- Subtract 3: \[ 0 - 3 = -3 \]
- Multiply by \( 1/2 \): \[ -3 \times \frac{1}{2} = -\frac{3}{2} \text{ or } -1.5 \]
-
For \( x = 5 \):
- Subtract 3: \[ 5 - 3 = 2 \]
- Multiply by \( 1/2 \): \[ 2 \times \frac{1}{2} = 1 \]
Step 2: Create Mapping
Now we can summarize these transformations in the mapping diagram format.
- Input: \( x \) | Transformation: Rule | Output: Result
- ------------------ | ------------------------ | -------------------
- \( -2 \) | Subtract 3: \( -5 \) then multiply by \( \frac{1}{2} \): \( -2.5 \) | \( -2.5 \)
- \( 0 \) | Subtract 3: \( -3 \) then multiply by \( \frac{1}{2} \): \( -1.5 \) | \( -1.5 \)
- \( 5 \) | Subtract 3: \( 2 \) then multiply by \( \frac{1}{2} \): \( 1 \) | \( 1 \)
Conclusion
The final mapping from input \( x \) to output \( y \) based on the provided rule is:
- From \( -2 \) to \( -2.5 \)
- From \( 0 \) to \( -1.5 \)
- From \( 5 \) to \( 1 \)
You can represent this visually as:
-2 → -2.5
0 → -1.5
5 → 1
This shows the relationship between the inputs and their corresponding outputs based on the applied rules.
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