Answer:
Shown below
Step-by-step explanation:
This function represents greatest integer function, which is the most famous of the step functions, which is denoted by [tex][x][/tex]. So, this function is defined as:
[tex]f(x)=[x] \ the \ greatest \ integer \ less \ than \ or \ equal \ to \ x.[/tex]. The graph of the greatest integer function has the following characteristics:
a) The domain of the function is the set of all real numbers.
b) The range of the function is the set of all integers.
c) The graph has a [tex]y-intercept[/tex] at [tex](0,0)[/tex] and [tex]x-intercept[/tex] in the interval [tex][0,1)[/tex]
d) The graph is constant between each pair of consecutive integers.
e) The graph jumps vertically one unit at each integer value.
[tex]f(x)=[x]-3[/tex] tells us that the original function has been shifted 3 units downward. So the correct option has been marked in the square red below.
