Evaluate Limit of Step Function

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Calculus
Section 2.3

I want to see the graph.
For part (b), I need (ii) and (iii) only.
Yes, part (c) is needed.

Screenshot_20220503-184619_Samsung Notes.jpg
 

The range of f(x)=[[cos x]], − π<=x< =π,where [[ ]] represent greatest integer function less than or equal to x is:

cos[x]=cos(−1)=cos1
cos[x]=cos(0)=1

Required range={cos1,1}
 

The range of f(x)=[[cos x]], − π<=x< =π,where [[ ]] represent greatest integer function less than or equal to x is:

cos[x]=cos(−1)=cos1
cos[x]=cos(0)=1

Required range={cos1,1}

I understand it is the Greatest Integer Function aka the Step Function. I thought the graph of the step function is like a ladder. No? I had no idea that this function can actually form the graph of a parabola.
 

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