S4
Functions & Mapping
Function → Rule
"If you can see a pattern, you can name it."
Philosophical Origin：Euler function concept
Minimal Example
Each input 2 gives output 4; input 3 gives output 6. This is f(x)=2x.
One-Line Rule
"Functions are patterns with names."
Common Misconception vs Correct Understanding
Functions are complex formulas.
Functions are input-output rules.
🌱 Growth Steps (Natural Evolution)
1 / 5 步
1
Mapping: Input → Output
✨ Starting Point: Growth begins here
如果你能 ↑ 那么你就能 ↓
2
Function notation: f(x)
如果你能 ↑ 那么你就能 ↓
3
Linear functions: Constant rate of change
如果你能 ↑ 那么你就能 ↓
4
Composite functions: Chain of transformations
如果你能 ↑ 那么你就能 ↓
5
Inverse functions: Reverse mapping
SAT Example Question
Question:
If f(x)=3x-1, what is f(5)?
Answer:
14
Explanation:
f(5) = 3×5 - 1 = 14
Practice Questions
5 questions with multiple solution methods
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