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Say you have a few functions on the same graph that oscillate, but they're not sine functions, they're polynomials.

curves

(These are Legendre polynomials) How do you refer to the "curvier" ones without sounding too informal? Is it ok to say "the curves that oscillate faster", even though these are not sinusoids? (I thought only sinusoids really "oscillate")

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Oscillation is closely related with rapid change, rapid change means the derivative is larger (in its absolute value). –  Asaf Karagila Oct 23 '12 at 0:51
    
Maybe the word is frequency? –  sidht Oct 23 '12 at 1:00
    
I don't think a polynomial has a frequency.. ? These functions are polynomials, so are not periodic, so I do not think they can have frequency. –  bobobobo Oct 23 '12 at 1:38
    
I've heard of less oscillations being descibed as smooth...perhaps "rough" would describe the opposite? –  Matt Groff Oct 23 '12 at 3:21
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1 Answer

Perhaps you can refer to it as "the curve with more inflection points", "the curve with more extrema", or "the larger degree polynomial".

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