Dependent and Independent Variables
Date: 05/24/2005 at 22:22:27 From: Miguel Subject: Is the Z variable dependent or independent? In a function, X is considered independent and Y is dependent. What is the Z variable? It's obvious that X is independent and Y is dependent...but Z makes no sense to me. I guessed "codependent", but maybe not.
Date: 05/24/2005 at 23:33:00 From: Doctor Peterson Subject: Re: Is the Z variable dependent or independent? Hi, Miguel. It depends on the function you have in mind! The variables x and y are not necessarily independent and dependent respectively; it is just tradition that calls for that. There is nothing wrong with defining a function as f(y) = 2y - 1 so that if x = f(y), y is independent and x is dependent. Note that in the definition of the function, x is really just a placeholder; I could have written it as "f(t) = 2t-1" or "f(z) = 2z-1" and the function would still be the same thing. Presumably you are thinking of an equation like y = 2x - 1 as representing a function you want to graph. But again, you can just as well graph the function x = (y + 1)/2 in which y is independent and x is dependent. Similarly, z can come into an equation in various ways. For example, you might define a SURFACE z = f(x,y) where, for each value of the pair (x,y), there is one value of z "above that point" on the surface; then x and y are BOTH independent, and z is dependent. But you could instead define a CURVE this way: y = f(x), z = g(x) so that for each value of x, there is a pair (y,z) on the curve. Then x is independent and y and z are BOTH dependent. And you can also define a curve this way (a parametric equation): x = f(t), y = g(t), z = h(t) so that ALL THREE variables are dependent on a "time" variable t. So there is nothing inherent in any variable that makes it dependent or not; and even convention does not dictate what role each will play. But z does tend to be dependent, and x to be independent, just by tradition. Did you have some particular function in mind? - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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