Answer:
The equation which matches the graph of the greatest integer function given is:
C) [tex]y=[x]+3[/tex]
Step-by-step explanation:
From the graph we may observe that:
when x=0
then the value of the function is: 3
Hence, we will put the value of x in each of the given options and see what holds true.
A)
[tex]y=[x]-3[/tex]
when x=0 we have:
[tex]y=[0]-3\\\\i.e.\\\\y=-3\neq 3[/tex]
Hence, option: A is incorrect.
B)
[tex]y=[x]+1[/tex]
when x=0 we have:
[tex]y=[0]+1\\\\i.e.\\\\y=1\neq 3[/tex]
Hence, option: B is incorrect.
D)
[tex]y=[x]-1[/tex]
when x=0 we have:
[tex]y=[0]-1\\\\i.e.\\\\y=-1\neq 3[/tex]
Hence, option: D is incorrect.
C)
[tex]y=[x]+3[/tex]
when x=0 we have:
[tex]y=[0]+3\\\\i.e.\\\\y=3[/tex]
Similarly all the other values hold for this function.
and the graph of this function matches the given graph.
