Re: Plot results not right

• To: mathgroup at smc.vnet.net
• Subject: [mg89968] Re: Plot results not right
• From: Helen Read <hpr at together.net>
• Date: Wed, 25 Jun 2008 06:28:53 -0400 (EDT)
• References: <g3nhbc\$g6\$1@smc.vnet.net> <g3q7od\$am7\$1@smc.vnet.net>

```Jean-Marc Gulliet wrote:
> BrenB wrote:
>
>> 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?
>
> Are you sure that the function you want to plot is this one? I might
> have missed something, but, since you mentioned you are taking a class
> in Calculus, I think you are studying real functions of a real variable
> (i.e. functions from R to R).
>
> The function f[x_] := 2 x - 3 x^(2/3) + 4 is defined on R+ only (i.e.
> for x positive or null) and is positive on this interval. Thus the
> function is always above the x-axis and can be drawn (or make sense)
> only for x >= 0.

This isn't true. x^(2/3) is defined for all reals, provided you take the
real cube root of x as we do in calculus class. Mathematica, however, by
default takes the principal root, which is complex for x<0, which is why
it doesn't plot anything for x<0. Unfortunately, there isn't an option
one can set that would force Mathematica to take the real root, but as I
and several others pointed out, you can get around it in this example by
plotting 2x - 3(x^2)^(1/3) + 4. As another example, where the power is
rational with numerator and denominator both odd, say x^(5/3), you can
get the desired result for x<0 by plotting Sign[x] Abs[x]^(5/3)

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