You are required to graph a translated version of the floor function, i.e. a function that returns the nearest integer which is less than or equal to the input.
So, this function maps every integer onto itself, and every decimal number to its integer part.
For example, [tex] f(4.547) = 4 [/tex], [tex] f(-12.987) = -13 [/tex] and [tex] f(1.23) = 1 [/tex]
Since you want to graph [tex] f(x) = \lfloor x \rfloor -1 [/tex], that "-1" translates the graph down one unit.
So, using the same examples as before, you have [tex] f(4.547) = 3 [/tex], [tex] f(-12.987) = -14 [/tex] and [tex] f(1.23) = 0 [/tex]
Also, as a consequence, every integer is mapped to the integer before: [tex] f(n) = n-1 [/tex].
So, the correct answer is the first one.
