Re: Re: Log(ln) Function + 2 Parameters + Greater

*To*: mathgroup at smc.vnet.net*Subject*: [mg89309] Re: [mg89298] Re: Log(ln) Function + 2 Parameters + Greater*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Thu, 5 Jun 2008 00:43:00 -0400 (EDT)*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst*References*: <g22tp5$ikl$1@smc.vnet.net> <g237c4$q2n$1@smc.vnet.net> <200806040937.FAA18315@smc.vnet.net>*Reply-to*: murray at math.umass.edu

f[a_,x_] is a function with two arguments, the first of which is being regarded as a "parameter". f[a_] is a function with one argument, whose value for a given "a" is a function to which you can input a value of x. So the construct f[a_][x_] captures more precisely the idea of a family of functions parameterized by parameter "a". Jerry wrote: > Sir, I have never seen a function definition in the form you > give: > f[a_][x_] := x (a + Log[x])^2 > > After a bit of playing with it, I don't see the difference > between this and > > f[a_,x_] := x (a + Log[x])^2 > > I really don't know how to search in help for this f[a_][x_] > form. Can you tell me if there is any essential difference? > > Thank you. > > > David Park wrote: >> First, define your f function with a as a parameter. >> >> f[a_][x_] := x (a + Log[x])^2 >> >> Mathematica can't make a plot unless it knows values for a. Of course, it >> won't plot any results for x < 0 and I'm not certain if you actually meant x >> > 0 rather than a > 0. In any case, you can use any real domain for a. Here >> is a plot for a specific value of a. >> >> Plot[f[2][x], {x, -5, 5}, >> AxesLabel -> {x, f}] >> >> You can look at an extended a domain by using Plot3D. >> >> Plot3D[f[a][x], {a, -5, 5}, {x, 0, 5}, >> PlotRange -> All, >> AxesLabel -> {a, x, f}] >> >> Another approach is to use a Manipulate statement with a controlled by a >> slider. >> >> Manipulate[ >> Plot[f[a][x], {x, 0, 5}, >> PlotRange -> {0, 250}, >> AxesLabel -> {x, f}], >> Style[Row[{HoldForm[f["a"][x]] == f["a"][x]}], 16], >> Delimiter, >> {a, -5, 5, Appearance -> "Labeled"}] >> >> >> > -- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305

**References**:**Re: Log(ln) Function + 2 Parameters + Greater***From:*Jerry <Jer75811@yahoo.com>