📈 Functions & Graphs

Last Updated: 06-Sep-2025

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."

Function Notation

We write functions like:

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

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.

Graph of a Function

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

👉 Example: f(x) = 2x then Table

xy = 2x
12
24
36
48
  • Graph is a straight line passing through (0,0).

Types of Graphs (Basic)

  • Linear function → f(x) = mx + c → straight line.
  • Quadratic function → f(x) = x² → 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."

⚡ 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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