how can you plot this?

Question

$y= \frac{x^3}{|x|}$ where x is not equal to 0.

i tried plotting in wolfram alpha and it shows a $x^3$ graph and i dont understand where the $x$ in the bottom goes? shouldn't it be $x^2$? anyways any kind of help is appreciated!

Answer 1

Well for $x<0$ you get $y=-x^2$ and for $x>0$ you get $y = x^2$. This is similar to the $y = x^3$ curve but not quite the same. You will notice when you plot all three simultaneously.

See the plot here: green is $y=x^3$, blue is $y=x^2$ and red is $y=\frac{x^3}{|x|}$