If I say “y is proportional to x,” I mean y = kx.
If I say “y is proportional to the square of x,” I mean y = kx^2.
If I say “y is proportional to the cube of x,” I mean y = kx^3.
Is there a general term for “y = kx, or y = kx^2, or y=kx^3, etc”. In other words, as y increases, x increases, but you don’t know exactly what the relationship is?
y increases monotonically as a function of x.
y correlates positively with x
This may be a nitpick, but if y = kx[sup]2[/sup], you can’t say y increases whenever x increases if there’s a possibility that x could be negative.
It’s probably a weaker condition than what you’re looking for, but you can say that y [symbol]Î W/symbol. What this means is that there are constants n and c such that, whenever x > n, y > cx.
How about y is proportional to a polynomial in x… (k, kx, kx^2,… are all polynomials in x as are any linear superposition)
I think “monomial” or even “monomial with positive coefficient” might be better, because -x^2+12x-5 is a polynomial, but doesn’t seem to fit here.
Here areplots of the equations with k = 3 and x running from -2 to 2 in steps of 0.1. Is there anything that describes all three other than that they are functions of x?
Everyone had great answers to the question as I actually asked it, but this is what I was looking for (the cases in which I want to use it fit the conditions necessary to make this true, and I’m looking for something that the reader could grok without having to learn any new words, only a new way to put those words together). Thanks!
Saying that y correlates positively with x allows for many more relationships than the ones you mention (y = k*log(x), y = k[sup]x[/sup], etc.), so be careful how you use it.
Yeah. It’s what I meant to ask for. For example, if someone has two data points, something like (1,2) and (2,4), they can say y seems to correlate positively with x, but they can’t really say anything more until they gather more data (and, of course, they can’t even say that with any certainty). That’s all I needed 
