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Left-Side and Right-Side Continuous

We define the floor function [[x]] to be the greatest integer not exceeding x. For example[[4]]=4
[[2.37]]=2
[[-1]]=1[[-1.2]]-2

Sketch by hand the graph y=[[x]] by first tabulating the values pf [[1]] for several numbers x. Then compare your graph with the plot from a graphing calculator. What are the discontinuities of f(x)=[[x]] where the domain of x is -2.3,=x,=1.5? Are these removable discontinuities? At the number x where f(x) is not continuous is f(x) continuous from the right? Is f(x) continuous from the left?

Solution Summary

Left Side and Right Side Continuity are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

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