Question

Which equation matches the graph of the greatest integer function given below?

A. y= [x] + 3
B. y= [x] -3
C. y= [x] +2
D y= [x] -2

Answer 1

D y= [x] -2

Explanation:

The "floor" or "greatest integer" function graphs as a step function with a solid dot at the left end of each step. The point (0, 0) is one of those solid dots. When 2 is subtracted from the function value, the graph is shifted down 2 units so that it looks like the one given.

The given graph is of the equation ...

`\boxed{y=\lfloor x\rfloor -2}`

_____

Additional comment

The ceiling function ...

`y=\lceil x\rceil`

graphs as a step function with a solid dot at the right end of each step. There is a solid dot at (0, 0) for this function, as well.

Note that the function symbols have "hooks" above or below the argument to indicate ceiling or floor (respectively). The use of a square bracket [ ] for either of these functions would need to be accompanied by an explanation of the intended meaning. By itself, a square bracket has "hooks" both at the top and bottom, so does not represent either function unambiguously.