📈 Functions & Graphs

Last Updated: 06-Sep-2025

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What is a Function?

A function is a rule that takes an input, does some operation, and gives an output.

👉 Example:

• Rule: "Multiply by 2"
• Input → 3 → Output → 6
• In math: $f(x) = 2x$

Hinglish Tip 🗣 : Function = "Machine jisme number daalo aur rule ke hisaab se naya number nikalo."

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Function Notation

We write functions like:

• $f(x) = x + 5$ → means: take x, add 5.
• If x = 2 → $f(2) = 2 + 5 = 7$.

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Examples

1. Mobile recharge
   • Base cost ₹50 + ₹10 per GB.
   • Function: $f(x) = 50 + 10x$ (x = GB used).
2. Temperature conversion
   • Celsius to Fahrenheit: $f(C) = (9/5)C + 32$.
   • If C = 0 → $f(0) = 32$.

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Graph of a Function

A graph shows the relation between input (x) and output (y).

👉 Example: $f(x) = 2x$ then Table

• Graph is a straight line passing through (0,0).

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Types of Graphs (Basic)

• Linear function → $f(x) = mx + c$→ straight line.
• Quadratic function → $f(x) = x^2$ → U-shaped curve (parabola).
• Constant function → $f(x) = 5$ → horizontal line.

Hinglish Tip 🗣 : Graph = "Table banake x aur y ko paper par dots lagao, line khinch jaayegi."

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Quick Practice

1. If $f(x) = x + 3$, find $f(5)$.
2. If $f(x) = 2x$, complete the table for x = 1, 2, 3, 4.
3. Draw the graph of y = x (hint: line through origin with slope 1).
4. Temperature in Celsius is 30. Use $f(C) = (9/5)C + 32$ to find Fahrenheit.

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