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Linear Functions Tables
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Linear Functions Tables
🎯 WALT: We Are Learning To
Today we are learning to:
- Generate tables of values using linear functions
- Understand how function machines work with inputs and outputs
- Recognise patterns in linear relationships
🔧 Part 1: Function Machine Practice
1. Complete this function machine table. The rule is: multiply by 3, then add 2
Rule: x × 3 + 2 = y
| Input (x) | Output (y) |
|---|---|
| 1 | _____ |
| 2 | _____ |
| 3 | _____ |
| 4 | _____ |
| 5 | _____ |
2. What pattern do you notice in the outputs? Describe it in your own words:
3. Complete this table for the rule: multiply by 2, then subtract 1
Rule: x × 2 - 1 = y
| Input (x) | Output (y) |
|---|---|
| 0 | _____ |
| 1 | _____ |
| 2 | _____ |
| 3 | _____ |
| 4 | _____ |
4. Choose the best description of what happens to the output (y) as the input (x) increases by 1:
The output increases by 1
The output increases by 2
The output increases by 3
The output stays the same
📊 Part 2: Real-Life Linear Functions
5. Sarah saves $4 every week. Complete the table to show her total savings:
| Weeks (x) | Total Savings ($) |
|---|---|
| 1 | $_____ |
| 2 | $_____ |
| 3 | $_____ |
| 4 | $_____ |
| 5 | $_____ |
6. A plant grows 3 centimetres each day. It starts at 5 cm tall. Write the rule and complete the table:
Rule: Height = _____ × (number of days) + _____
| Days | Height (cm) |
|---|---|
| 0 | _____ |
| 1 | _____ |
| 2 | _____ |
| 3 | _____ |
7. Look at your completed tables above. Which statements are true about linear functions? (Tick all that apply)
The output increases by the same amount each time
The pattern makes a straight line when graphed
You can predict future values using the pattern
The relationship between input and output changes randomly
8. Create your own linear function rule and complete the table:
My rule: y = _____ × x + _____
Describe your rule in words: _________________________________
| Input (x) | Output (y) |
|---|---|
| 1 | _____ |
| 2 | _____ |
| 3 | _____ |
| 4 | _____ |
9. Reflection: Explain in your own words what makes a function "linear":
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