Greatest integer function f(x) = [x]महत्तम पूर्णांक फलन f(x) = [x]Greatest integer function f(x) = [x]

NCERT Exercise 1.2 · Class 12 Maths · Chapter 1 · interactive diagram

Parts and what they mean

• x-axis (x-अक्ष) — The horizontal number line; inputs x are read here.
• y-axis (y-अक्ष) — The vertical number line; outputs y = f(x) are read here.
• Origin O(0, 0) (मूल बिंदु O(0, 0)) — Where the two axes cross.
• Steps of y = [x] (y = [x] की सीढ़ियाँ) — [x] is the greatest integer ≤ x, e.g. [1.5] = 1, [−0.5] = −1. Many x give the same value: not one-one.
• Filled dot = included (भरा बिंदु = शामिल) — At x = 1, [x] = 1 (the left end of each step belongs to it).
• Hollow dot = not included (खाली बिंदु = शामिल नहीं) — Just before x = 2 the value is 1, but at x = 2 it jumps to 2.
• y = 0.5 is never an output (y = 0.5 कभी आउटपुट नहीं) — Outputs are only integers, so f : R → R is not onto.

Original diagram drawn by Simple Learning Hub, based on NCERT Exercise 1.2. Report a mistake