Functions

Think of a function as a machine that takes something in, does some work on it, and then gives something out.

🚗 Everyday Analogy: The Function Machine

Imagine a machine where:

• You input a number (like putting an ingredient into a blender).
• The machine processes it in a specific way (e.g., doubles it, adds 5, squares it).
• It outputs a new number (like getting a smoothie after blending).

For example, if the function is “double the input”, it works like this:

• Input: 3 → Output: 6
• Input: 5 → Output: 10

This can be written as: f(x)=2xf(x) = 2x

where f(x) means “the function of x.”

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🎯 Key Points About Functions

✅ Each input has exactly one output → No confusion, one input gives only one result.
✅ The rule stays the same → If the function is “add 5,” then every input follows that rule.
✅ Functions can be anything → Doubling, squaring, adding, subtracting, even something like “if x is a cat, return ‘meow’!”

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📊 Real-Life Examples of Functions

1️⃣ Temperature Conversion

• Celsius to Fahrenheit: F(x)=(9/5)x+32F(x) = (9/5)x + 32
• If you input 0°C, the output is 32°F.
• If you input 100°C, the output is 212°F.

2️⃣ Monthly Salary Calculation

• Suppose your hourly pay is $10, and hours worked is h: Salary(h)=10hSalary(h) = 10h
• If you work 40 hours, you earn $400.

3️⃣ Speed Calculation

• If speed is distance ÷ time, then: Speed(t)=100tSpeed(t) = \frac{100}{t}
• If you take 2 hours to travel 100 km, your speed is 50 km/h.

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🔢 Fun Challenge

If a function is f(x) = x² + 3, what happens when you input:

• 2?
• 5?
• -1?

Hope you will have got the answers.