
1. Re: Is there something wrong with my Grapher？
AveMaleficum Nov 28, 2012 7:48 AM in response to AveMaleficumMy question is,these two equations are the same,right?
But why the first equation only show x on positive x axis?
Did I do something wrong?

2. Re: Is there something wrong with my Grapher？
Linc Davis Nov 28, 2012 10:37 AM in response to AveMaleficumThe functions are not the same. In the first case, you're raising a real number to a fractional power. That's ambiguous for negative arguments, so the program only graphs it for nonnegative arguments. In the second case, you're raising a nonnegative number to a fractional power.

3. Re: Is there something wrong with my Grapher？
AveMaleficum Nov 28, 2012 3:47 PM in response to Linc Davis 
4. Re: Is there something wrong with my Grapher？
Linc Davis Nov 28, 2012 4:05 PM in response to AveMaleficumI agree, that's inconsistent.

5. Re: Is there something wrong with my Grapher？
AveMaleficum Nov 29, 2012 1:27 AM in response to Linc DavisAnd more examples
Is this a big bug in Grapher?I will keep this post updated.
Here are some polynomial examples.
Anothe set

6. Re: Is there something wrong with my Grapher？
AveMaleficum Nov 29, 2012 1:53 AM in response to Linc Davis 
7. Re: Is there something wrong with my Grapher？
AveMaleficum Nov 29, 2012 1:56 AM in response to Linc DavisAnd change 3 to 5
It seems that Grapher only shows function on whole domain when exponent is integer.

8. Re: Is there something wrong with my Grapher？
YB24 Nov 29, 2012 6:51 PM in response to AveMaleficumHi AveMaleficum !
It is NOT inconsistent at all Mr. Linc Davis : just go back to the mathematical definitions !
Generally, by definition, rational exponents p = m / n can be applied only to a positive number as says :
http://www.edu.upmc.fr/physique/lp326/dossiers/mathchap5.pdf (French but easy to translate) or Wikipedia :
« Limits of rational exponents
Since any irrational number can be approximated by a rational number, exponentiation of a positive real number b with an arbitrary real exponent x can be defined by continuity with the rule… »
in http://en.wikipedia.org/wiki/Exponentiation#Limits_of_rational_exponents
Same rule for real exponents : try y = x^π for example.
But if p is an integer a^p a > or < 0, if p = 1 / n with n an odd integer, a^(1/n), a may be < 0.
See your math book, please.
Grapher wants x > 0 for real exponents as well. With rational exponent m / n, you may cheat to get a full curve for all x values : use y = (x^(1/3))^7 or (x^7)^(1/3) or or (third root x)^7 (radicals and ^ allowed) instead of x^(7/3).
So this is not a new Grapher's bug.
Enjoy,
YB24