Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.

share|cite|improve this question
From $\epsilon$ to $1$ since you have a problem when $x>1$. – Claude Leibovici Mar 29 '14 at 14:29
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 $f$.)

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.