The equation that matches the graph of the greatest integer function given is:
C.) y=[x]-4
Clearly after looking at the graph of the function we see that:
when x=2 the value of function is: y= -2
Hence, we will check by putting the value of x in each of the following options and check which hold true.
A.)
y=[x]+2
when x= 2 we have:
[tex]y=[2]+2\\\\y=2+2\\\\y=4\neq -2[/tex]
Hence, option: A is incorrect.
B.)
y=[x]-2
when x= 2 we have:
[tex]y=[2]-2\\\\y=2-2\\\\y=0\neq -2[/tex]
Hence, option: B is incorrect.
D.)
y=[x]+4
when x= 2 we have:
[tex]y=[2]+4\\\\y=2+4\\\\y=6\neq -2[/tex]
Hence, option: D is incorrect.
C.)
y=[x]-4
when x= 2 we have:
[tex]y=[2]-4\\\\y=2-4\\\\y=-2[/tex]
Similarly for other value of x it will match.
Hence, option: C is the correct answer.
