Function machines and reversing operations · Higher
導入済み| English | 意味 |
|---|---|
| input/ˈɪnpʊt/ | 入力値 |
Which input produced the output?
- A machine doubles a number then adds three. Which starting number would produce eleven?
- This lesson studies input 输入值: The value supplied to a rule before its operations are carried out.
Choose the mathematical structure
- Follow the operations in their stated order. To recover a starting input, undo the final operation first. A table pairs each input with its output. The same starting input must have only one output for the rule to be a function.
- State the allowed inputs and units before calculating. An equation should express the relationship, not just record a calculator entry.
To reverse "double then add 3", what is the correct inverse sequence?
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
Reverse operations undo the LAST forward step first: output 11 minus 3 gives 8, then halving gives 4. Undoing in the wrong order gives 4 then 1 - not the input.
Work through a checked case
- Check the result against the starting quantities. Substitute into the original relation, or compare the graph and numerical answer where appropriate.
Input 4 gives 2×4+3=11. To reverse output 11, subtract 3 to get 8 then divide by 2 to get 4. Inputs -1,0,1 give outputs 1,3,5. If a second machine squares its input, passing 4 through the first then the second gives 11²=121; reversing their order gives 2×16+3=35.
Function machines and reversing operations
Follow the operations in their stated order
Compare the model with the worked case and explain one change.
Find the output of double then add 3 for input 4.
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
2×4+3=11.
Test a tempting shortcut
- Reversing the rule does not mean repeating it. The last forward step is the first reverse step. Different operation orders can produce different outputs.
- When a shortcut fails, identify the assumption it breaks. Keep an exact value until the requested final rounding.
Reversing double then add three means subtracting three only. This claim is false. Explain which definition or assumption it violates.
Find the input producing output 11.
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
Undo +3, then undo ×2: (11-3)/2=4.
Reversing double then add three means subtracting three only.
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
Reversing the rule does not mean repeating it. The last forward step is the first reverse step. Different operation orders can produce different outputs.
Interpret a new situation
- AQA A7 Foundation interprets simple functions as input-output rules. Higher also uses formal inverse and composite function notation in the separate function lesson.
- A complete solution gives the mathematical result and explains what it means. Check that it is possible in the stated context.
Find the output for input -1.
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
2×(-1)+3=1.
Match each machine stage of 2x+3 to its role.
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
A function pairs each input with exactly one output, so the inverse is well defined when the operations are undone in reverse order.
Use this in your course
- 8300 · Higher · 3.2. Match the target tier and specification before assigning extensions.
- Give the method before the final answer, and use the paper's calculator and formula rules. Review a wrong answer by locating the first invalid step.
The value supplied to a rule before its operations are carried out. Choose the relationship, show the method, check its assumptions and interpret the result.