4.1 Piecewise Functions
Piecewise functions are defined by different functions throughout the different intervals of the domain.
Example :
f(x) ={■(3x for x>0@2 for x =0@-2x for x <0)┤

4.2 Absolute/Modulus Function

If x ∈ R ; the absolute value of x, noted |x| is defined as follows :
|x|=x if x ≥ 0
|x|=-x if x≤0
Graph of y=|x|

Examples : |20|=20
|-3|=3
|1-π|=π-1 as 1-π <0
Properties :
Absolute value of a product : |xy|= |x| |y|
Absolute value of a quotient : |x/y|= |x|/|y|
Triangular inequality :
|x+y|≤ |x|+ |y|

4.3 Ceiling Function
The symbol for a ceiling function is
⌈2.31⌉
And ⌈2.31⌉= 3
Graph of y=⌈x⌉