What is a Function?

Description

Illustrates the concept of a function as a "machine" that takes an input and produces an output. Shows the double() function called multiple times with different inputs, demonstrates reusability, and briefly connects to mathematical function notation.

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Phases

#	Phase Name	Duration	Description
1	Title Card	3s	Title animates in
2	The Machine	5s	Box labeled "double(x)" appears with input/output slots
3	Input 3 → 6	6s	Number 3 travels into machine, 6 emerges
4	Input 7 → 14	6s	Number 7 travels in, 14 emerges
5	Reusability	5s	Same machine box called again with new values; highlight "reuse"
6	Math Connection	5s	Show f(x) = 2x notation next to machine
7	More Complex Function	6s	New machine box: greet(name) → "Hello, Alice!"
8	Outro	3s	Fade out

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Layout

+------------------------------------------------------+
|             What is a Function?                     |
+------------------------------------------------------+
|                                                      |
|  INPUT                                               |
|    3  ──>  [ double(x)  ]  ──>  6   OUTPUT          |
|    7  ──>  [            ]  ──>  14                   |
|                                                      |
|  Mathematical notation:  f(x) = 2x                  |
|                                                      |
|  "Alice" ──>  [ greet(name) ]  ──>  "Hello, Alice!" |
|                                                      |
|  KEY IDEA: Write once, reuse many times!            |
+------------------------------------------------------+

Area Descriptions

• Top: Title
• Center: Large machine box (dark background, cyan border)
• Left: Input values with arrow pointing right into machine
• Right: Output values with arrow pointing right out of machine
• Bottom: Math notation and reusability message

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Assets & Dependencies

• Fonts: LaTeX / sans-serif
• Manim version: ManimCE 0.19.1

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Notes

• The machine box has a "gear" feel — slightly ornate border
• Inputs travel as animated dots/numbers along an arrow path
• Output appears with a pop (scale up then settle)
• Math connection uses MathTex for f(x) = 2x