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

The 3rd graph i.e.) the graph with points (-3,-6), (-2,-5), (-1,-4), (0,-3), (1,-2), (2,-1) and (3,0) represents the function f(x)=[x]-3 over interval [-3,3].

Step-by-step explanation:

The given interval is -3 to 3 and substitute these values in the given function.

The given f(x)=[x]-3,

If x= -3,

f(x)= -3-3.

f(x)= -6.

If x= -2, f(x)= -5.

If x= -1, f(x)= -4.

If x= 0, f(x)= -3.

If x=1, f(x)= -2.

If x=2, f(x)= -1.

If x=3, f(x)=0.

The points are (-3,-6), (-2,-5), (-1,-4), (0,-3), (1,-2), (2,-1) and (3,0).

Plot the points in the graph.

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step-by-step explanation:

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