The graph in the represents the function
Further explanation:
The function is given as follows:
Label the above equation as follows:
                     (1)
In the above equation represents a greatest integer function.
Greatest integer function is a function which is an integral part of any real number .
If is an integer than is also the same integer and if is in decimals than the value of is the next smallest integer.
For example: If than and if than
Figure 1 (attached in the end) indicates the graph of the function .
The function is and the interval is given as .
Substitute in equation (1).
Substitute in equation (1).
From the above calculation it is concluded that for each value of in the interval the value of the function is .
Substitute in equation (1).
Substitute in equation .
From the above calculation it is concluded that for each value of in the interval the value of the function is .
Similarly, the value of the function in the interval and are and respectively.
Substitute in equation (1).
Only for the value of the function is .
The value of the function for different value of lying in different intervals is given in the table attached in the end of the solution.
Option A:
From the graph given in the option A it is observed that the value of the function in the interval is which is incorrect because as per the table 1 (attached in the end) the value of the function in the interval is .
This implies that the option A is incorrect.
Option B:
From the graph given in the option B it is observed that the value of the function in the interval is which is incorrect because as per the table 1 (attached in the end) the value of the function in the interval is .
This implies that the option B is incorrect.
Option C:
From the graph given in the option C it is observed that the value of the function for all the values of in the interval is , in the interval is , in the interval is and so on.
The value of the function as observed from the graph in option C for different intervals is exactly same as the calculation made above.
This implies that option C is correct.
Option D:
As per the our calculation the value of the function in the interval is  .
But from the graph in option D it is observed that for all value of in the interval the value of the function is which is not correct.
This implies that option D is incorrect.
Therefore, the graph in the represents the function .
Learn more:
1.A problem on composite function Â
2.A problem to find radius and center of circle Â
3.A problem to determine intercepts of a line Â
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Functions
Keywords: Functions, greatest integer function, floor function, domain , range, intervals, equation, graph, curve, relation, F(x)=[x]-3, [x], smallest integer function, ceiling function.