Fractional Part Function – Graph, Domain and Range

Here you will learn definition, graph, domain and range of fractional part function.

Let’s begin –

Fractional Part Function

Definition : For any real number x, we use the symbol {x} to denote fractional part or decimal part of x.

For example, {3.45} = 0.45, {-2.75} = 0.25, {-0.55} = 0.45, {3} = 0, {-7} = 0 etc.

The function f : R \(\rightarrow\) R defined by f(x) = {x} for all x \(\in\) r is called the fractional part function.

It is evident from the definition that

f(x) = {x} = x – [x] for all x \(\in\) R

Also Read : Types of Functions in Maths – Domain and Range

Graph of Fractional Part Function

The graph of the fractional part function is as shown below.

fractional part function

Domain and Range of Fractional Part Function

We observe that the domain is the set of R of all real numbers and the range is the set [0, 1).

Domain : R

Range : [0, 1)

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