FUN004 · Functions & graphs · Classes 9–12
Identity Function
The identity function returns its input unchanged. Its graph is the line y = x through the origin at 45°.
y = xIdentity Function
📐 Formula
f(x) = x; domain and range: all real numbers
✏️ Worked example
f(3) = 3, so the point (3, 3) lies on the graph.
🌍 Where it is used
A mirror line: a graph and its inverse are reflections in y = x.
❓ Quick check
For the identity function, f(−2) = ?
🏋️ Practice
Easyf(7) = ?
Answer: 7
MediumWhat angle does y = x make with the x-axis?
Answer: 45°
ChallengeWhich function, composed with any f, leaves f unchanged?
Answer: The identity, f(x) = x