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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.

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    What about $f(x)=x^n$ for $1 \leq n \leq 26$?2011-11-06
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    It's hard to tell, without looking at a scale, $x^5$ from $x^7$ say.2011-11-06
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    What do you mean by "scale" ? ;) If you think you need to increase the scale, look at $f(x)=1000x^n$ ;)2011-11-06
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    Your example is a bit questionable in my opinion because one could argue that $x^3$ and $x^5$ are not markedly different either. But if consider $f_n(x) = x(x-1)\ldots(x-n)$, you can tell their graph apart instantly by counting their roots ($f_n$ has $n+1$ roots).2011-11-06
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    Like, $x^2$ and $x^3$ are obviously different graphs, without looking at any numbers, right? Any way that you graph them? Same, to a lesser extent, with $x^2$ and $x^4$—one of them is perfectly parabolic, the other is more squarish.2011-11-06
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    Eh, I'd rather use orthogonal polynomials instead of power functions...2011-11-06
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    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

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