       Re: Re: The graph of (x + 2)^(1/5) + 4 not plotted correctly

• To: mathgroup at smc.vnet.net
• Subject: [mg103938] Re: [mg103926] Re: The graph of (x + 2)^(1/5) + 4 not plotted correctly
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Tue, 13 Oct 2009 23:17:45 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <868306d90910120643u7f1c2299v2cd1845508dc85b7@mail.gmail.com> <200910131118.HAA29247@smc.vnet.net>

```Could you please just tell us what you think is wrong with the plot that
Mathematica provides?

I ask because when I point my browser to the link you provide...

(1) I get a large number of annoying (and potentially dangerous)
3rd-party ad-generating items on the URL page that clamor to be allowed
to do their thing.

(2) The plot finally displayed is of something entirely different -- of
exp(-x^2) and its first two derivatives.

As to the function (x + 2)^(1/5) + 4 that you asked about: Did you just
try something like the following?

Plot[(x + 2)^(1/5) + 4, {x,-7,5}]

If so, then you were probably surprised that the graph ended on the left
at x == -2.  And that is precisely what Mathematica should be expected
to do. After all, Mathematica "wants" numbers to be complex when they
can be.  And z^(1/5) denotes the PRINCIPAL 5th-root of z, so that when z
is negative, you do NOT get a negative real number, but rather the
non-real, complex principal 5th-root.

If you want the high school/calculus variety 5th-root function, then you
need to finesse this. For example:

f[x_] := Sign[x + 2] Abs[x + 2]^(1/5) + 4
Plot[ f[x], {x,-7,5}]

victor chg wrote:
> Here is the link to the image:
> http://tinypic.com/view.php?pic=veae6u&s=4
>
> Victor Chg

--
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

```

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