Fractional Part Function Graph

The graph of the Fractional Part Function, often denoted as {x} or frac(x), displays distinct characteristics. It represents the decimal part of a real number x and exhibits some notable features:

• Step Function: The graph consists of horizontal steps at integer values of x, indicating the abrupt change in the fractional part when x crosses an integer. At each integer, the fractional part resets to 0.
• Periodicity: The graph is periodic with a period of 1. This means that the pattern repeats every interval of 1 along the x-axis. The fractional part function is the same for x and x + 1, x + 2, and so on.
• Values between 0 and 1: The function’s range is between 0 (inclusive) and 1 (exclusive), reflecting the fact that the fractional part is always a decimal value between 0 and 1.
• Discontinuity at Integers: The graph has discontinuities at integer values of x, where there are vertical jumps. These jumps occur because the fractional part experiences an abrupt change at integer values.
• Symmetry: The graph is symmetric around the integers. This means that the portion of the graph to the right of an integer mirrors the portion to the left.

Fractional Part Function, often denoted as {x}, represents the decimal part of a real number x after removing its integer part. In simpler terms, it captures the fractional portion of a number, excluding the whole number component. The fractional part function is particularly useful in various mathematical contexts, such as number theory, analysis, and computer science, where understanding the non-integer portion of a number is essential.

In this article, we will learn about the various concepts related to the fractional part function, like the meaning and definition of the fractional part function, properties of the fractional part function, its formula, application, graph, and solved examples for better understanding.