Question

Which equation is shown in the graph?

y = [[x]]

y = [[x + 3]]

y = [[x]] ­- 3

y = |x ­- 3|

Answer 1

`y = floor(x+3)` which I guess in your notation is `y = [[x+3]]`

Explanation:

Note that the graph is flat most of the time, with single unit jumps.

That indicates that the floor function or ceiling function is in use.

Each line segment is left closed and right open, indicating that we want to use the floor function.

Note that `(-3, 0)` is one of the points of the graph of the function at the beginning of a unit interval.

Hence we can deduce that `y = floor(x+3)`, i.e. `y` is the greatest integer less than or equal to `x+3`.

I think your notation indicates the floor function by double square brackets, so in your notation:

`y = [[x+3]]`