Relations & functions
Values, domain and range, and counting relations.
Learn with Kutty
Go one screen at a time. Press Next when you are ready. Tap 🔊 Read to me to listen.
A function is a machine: one input in, exactly one output out.
Look: Square machine: each input has exactly one arrow out.
✏️ Your turn!
Type your answer and press Check. Kutty will tell you if it is right.
1f(x) = 3x − 1. f(2)?
2f(x) = x². f(−3)?
3Can 1/x take x = 0?
! Careful!
✗Two inputs cannot share an output.
✓They can (2² and (−2)² are both 4). One input just cannot have two outputs.
✗f(4) means f × 4.
✓It means "put 4 into f".
See the whole lesson on one page
A function is a machine: one input in, exactly one output out.
f(x) = x² means "put a number in, square it". The allowed inputs are the domain. The outputs you can get are the range.
Think of it like thisA juice machine: press button 2, get mango juice — every single time. One button never gives two different drinks.
Solved together
f(x) = 2x + 3. Find f(4).
Put 4 in wherever you see x.
2 × 4 + 3Work it out.
8 + 3 = 11
Answerf(4) = 11.
For older learners and grown-ups: a little more
Domain of 1/(x − 2) is all real numbers except 2; its range is all reals except 0. A relation is a function only if every input has exactly one output.
Now practise it
Kanakku makes new questions on relations & functions every time. It shows the working and gives a hint when you are stuck.