Modulus and integer-part functions
See the modulus in a table and on a graph, solve a modulus equation as two crossings with a line, read the steps of the integer-part (floor) function and plot a taxi fare that rises in steps.
- UK: Year 12
- France: grade 10
- Iran: grade 11
- Afghanistan: grade 10
- Palestine: grade 10
- Russia: grade 7
Guide
|x| is the distance from x to zero: always zero or positive. |x − 2| is the distance from x to 2. The equation |x − 2| = 3 asks for the points 3 away from 2: two answers.
The graph of y = |x − 2| is a V and never goes below the x-axis. The solutions of |x − 2| = 3 are where the graph meets the horizontal line y = 3.
The floor function [x] gives the largest whole number that is not more than x: [2.7] = 2 and f(−1.3) = −2. Its graph is a staircase: each step is closed at its left end and open at its right end.