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Question

Draw the graph of the greatest integer function:

f:RR:f(x)=[x] for all xϵR

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Solution

Using the definition of [x], we have

[x]=2, for 2x<1

[x]=1, for 1x<0

[x]=0, for 0x<1

[x]=1, for 1x<2

[x]=2, for 2x<3

[x]=3, for 3x<4.

Taking the scale: 10 small divisions = 1 unit, the graph of the function f(x)=[x] may be drawn as shown below.


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