Re: Plot results not right

• To: mathgroup at smc.vnet.net
• Subject: [mg89882] Re: Plot results not right
• From: magma <maderri2 at gmail.com>
• Date: Tue, 24 Jun 2008 03:20:10 -0400 (EDT)
• References: <g3nhbc\$g6\$1@smc.vnet.net>

```On Jun 23, 8:54 am, BrenB <GoogleGro... at ebesser.com> wrote:
> I'm new to Mathematica.
>
> I'm studying Calculus, and I'm trying to reproduce, in Mathematica,
> the graph results of an equation in my book.
>
> Plot[2 x - 3 x^(2/3) + 4, {x, -1, 6}]
>
> The output graph is correct, except there should be graphing in the
> 2nd and 3rd quadrant, and there is none.
>
> Is there another way to enter this equation into Mathematica to get
> the correct graph results?
>
> Thanks

This is because x^(2/3) is a function which does not have a unique value.
If you use Mathematica 6.x, or the equivalent section if you use prior
versions.

So x^(2/3) when x is -1 for example, is not = to 1, but it is a
complex number for Mathematica.
x^(2/3) has in effect 3 solutions, one of them is 1, but Mathematica prefers
another one.
Perhaps you do not know about complex numbers yet, do not worry, they
are not so complex.

You can see what is going on by evaluating

x^(2/3) /. x -> -1 // N

So in the end, if you want to plot your function for negative x, I
would suggest you replace x^(2/3) by Abs[x]^(2/3), that is

Plot[2 x - 3 Abs[ x]^(2/3) + 4, {x, -1, 6}]

This is because you have a square (the 2 in 2/3), so if you use
Abs[x]^2 is the same as x^2 and Mathematica will not complain

hope that helps

```

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