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I am confused on how to plot $f(x)=\frac{1}{\lfloor1/x\rfloor}$ where $\lfloor x\rfloor$ is the greatest integer function.

This is how I started: For $0<x<1$, $1<1/x<\infty$ and then I do not know what to do.

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From $\epsilon$ to $1$ since you have a problem when $x>1$. –  Claude Leibovici Mar 29 at 14:29

1 Answer 1

up vote 1 down vote accepted

Hints: Try breaking your function down into "smaller pieces".

If you have a general graph $y = g(x)$, do you have an idea what the graph $y = \lfloor g(x) \rfloor$ looks like? If not, draw a "typical" differentiable function $g$ on a sheet of lined paper, think of the lines as integer values, and use them to graph $y = \lfloor g(x) \rfloor$. :)

Now you should be able to graph $y = \lfloor 1/x \rfloor$ with no trouble. The final step is to graph the reciprocal, whose height at each point is your $f(x)$. This should be straightforward. (As Claude Leibovici notes, you'll need to consider which points are in the domain of $f$.)

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