The most famous of the step functions is the greatest integer function, which is denoted by . So, this function is defined as:
.
These are the characteristic of this function:
The domain of the function is the set of all real numbers.
The range of the function is the set of all integers.
The graph has a at and in the interval
The graph is constant between each pair of consecutive integers.
The graph jumps vertically one unit at each integer value.
However, we have made some changes to the parent function by multiplying it by 3 and making a shift 4 units downward. Finally, we get the graph shown below that matches the fourth option.