Which is the graph of y=[x]-2?

The function y = ⌊x⌋ is called the "greatest integer value" function.

it works as follows: the input is any number x, the output is the greatest  

integer smaller or equal to x.

For example:

⌊0.1⌋=0

⌊0.26⌋=0

⌊0.4678⌋=0

⌊0.8989⌋=0

⌊0.999⌋=0

⌊1⌋=0

⌊1.0001⌋=1

so, the value of ⌊x⌋, for the entire interval (0, 1] is 0.

Similarly,  

the value of ⌊x⌋, for the entire interval (1, 2] is 1.   and so on,  

thus the graph of  y = ⌊x⌋ is as shown in picture 1

the graph of   y = ⌊x⌋ – 2   is the graph of   y = ⌊x⌋   shifted 2 units down.

check picture 2.