Which graph represents the function over the interval [−3, 3] ? f(x)=⌈x+1⌉

We are asked to find which graph represent the function f(x)= over the interval [-3,3]

We know that the ceiling function has following properties:

" The ceiling function (also known as the least integer function) of a real number  x, denoted by is defined as the smallest integer that is not smaller than x ".

The graph of the function f(x) between [-3,3] is attached to the answer.

when x=-3 then f(x)= -2

The function will give the value between  -3<x≤-2  to be -1.

since when  -3<x≤-2 then -2<x+1≤ -1

Hence f(x)= -1

Similarly when -2<x≤-1 then f(x)=0

when -1<x≤0  then f(x)=1      

when 0<x≤1  then f(x)=2

when 1<x≤2  then f(x)=3

when 2<x≤3  then f(x)=4

The graph is attached to the answer.