0
$\begingroup$

Is there any function which produces at least 26 recognizably distinct graphs?

For example, $f(x) = x^n, n\geq0$ produces distinct graphs for for all positive integers $n < 6$. I'd like it to be obviously distinct without having to look at a scale.

$n$ should start at 0 or 1 (it should not be negative) and increment normally.

If this doesn't make sense, please ask for clarification.

  • 0
    Your title seems to ask for a *single* function; your post already talks about several different functions. Rather, it seems you are asking for some sort of "parametrized family" of functions that have clearly distinguishable graphs, or something like that.2011-11-06

1 Answers 1

1

If you're looking for an elementary family parametrized by nonnegative integers, you might try $f(x) = \sin(n x)/\sin(x)$ (defined to be equal to $n$ at the removable singularities $x = 0,\ \pi, \ldots$). Note that there are $n-1$ zeros between two high peaks (if $n \ge 3$ is odd) or between a high peak and a deep valley (if $n\ge 2$ is even).

  • 0
    I've fiddled with the integrals of the Bernoulli-polynomials a couple of years ago. I've done an overlay-plot of the first 18 such polynomials and the grouped by 4 and rescaled by tanh. Maybe you like this. See http://go.helms-net.de/math/pascal/bernoulli_en.pdf page 16 to see the plots and pages 9 to 11 for the descriptions of the functions.2011-11-06