Functions — Lesson
1) Hook — The Magic of Vending Machines
Imagine you go to a vending machine that gives you a chocolate bar when you insert exactly ₹20. If you put ₹10, nothing happens. If you put ₹20, you get one chocolate. If you put ₹40, you get two chocolates. Here, the machine follows a rule: For every ₹20 inserted, you get one chocolate. This is exactly how a function works — it takes an input and gives a unique output based on a rule!
2) Core Concepts — Understanding Functions
A function is a special relation where each input has exactly one output.
- Input (Domain): The set of values you put into the function.
- Output (Range): The set of values you get from the function.
- Rule: The formula or method that assigns the output to each input.
Example 1:
| Input (x) | Output (f(x) = 2x + 3) |
|---|---|
| 1 | 2(1) + 3 = 5 |
| 2 | 2(2) + 3 = 7 |
| 3 | 2(3) + 3 = 9 |
Example 2: Is this a function?
| Input (x) | Output (y) |
|---|---|
| 1 | 3 |
| 1 | 5 |
Here, input 1 gives two different outputs (3 and 5). So, this is not a function.
3) Key Formulas / Rules
Definition of a Function:
f: A → B means function f assigns each element of set A (domain) exactly one element of set B (range).
Function Notation:
f(x) = expression involving x
Example: f(x) = 3x - 4
How to check if a relation is a function?
- For every input, there must be only one output.
- Graphically, it passes the Vertical Line Test: no vertical line should cross the graph at more than one point.
4) Did You Know?
The word function was first used by the famous mathematician Leonhard Euler in the 18th century. In India, functions are used daily — for example, the fare of an auto-rickshaw depends on the distance travelled, which is a function of distance!
5) Exam Tips — Avoid These Common Mistakes!
- Do not confuse relations with functions: Remember, a function gives only one output for each input.
- Use function notation carefully: f(2) means substitute x = 2 in the rule.
- Vertical Line Test: When asked if a graph is a function, apply this test.
- Read questions carefully: Some questions ask for domain or range — write the correct set of input or output values.
- Practice with tables and graphs: Many board exam questions provide tables or graphs — analyze them thoroughly.
Mnemonic to remember function definition:
“Each Input Has Unique Output” → EIHU
Functions — Mcq
Functions — Mnemonic
Mnemonic 1: "F.A.N.C.Y" for Functions Basics 🎯
- F - First input (Domain value)
- A - Assign rule (The function’s formula)
- N - Number output (Range value)
- C - Check uniqueness (One input → one output)
- Y - Yields result (Function gives output)
Use this to remember: A function is like a FAN that always blows one way—one input, one output! 🌬️
Mnemonic 2: Hindi Rhyming Phrase for Function Definition 🎵
“Ek input, ek output ka khel,
Har baar same, na ho khel!”
Meaning: One input, one output game,
Every time same, no changing aim!
This reminds you that a function must give the same output for the same input every time.
Mnemonic 3: Funny Acronym "FUN" for Function Properties 😄
- F - Fix one output per input
- U - Unique output always
- N - No multiple outputs for one input
Remember: A function is always “FUN” because it’s fair and predictable! 🎉
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