3

$y = (x-4)^{2/3}$ is simple enough, right? By inspection, a cusp function with cusp at $(4,0)$ and a $y$ intercept of $16^{.333} = 2.52$, but...

When graphed on Desmos the above is what I see.

When graphed on Fooplot, only the right side of the cusp is shown.

When graphed on wolfram, at $x<0$, real part is negative and there is an imaginary part that I can't understand.

Can someone share their insight with me?

Micah
  • 38,108
  • 15
  • 85
  • 133
Chris Crawford
  • 53
  • see this question and the related answers at http://math.stackexchange.com/questions/25528/cubic-root-of-negative-numbers – user72272 Nov 07 '14 at 17:59

1 Answers1

2

Generally function $g(y)=y^a$, where $a$ is a positive constant, is well-defined for $y\geq0$. Hence your function is well-defined for $x\geq4$. For the other case, one may take additional assumptions and they are different in your programs, hence different results.

Przemysław Scherwentke
  • 13,668
  • 5
  • 35
  • 56