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.
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).