# Thread: Unfamiliar Cubed Root Function

1. ## Unfamiliar Cubed Root Function

I'm in Calculus AB and we are currently exploring the rules of derivatives. One function that they give, represented in the transcript of the lesson as $y = \sqrt[3]{x^2} + 1$ is first depicted in the attachment.

What the transcript gives and what the image shows are two different formats; what exactly does the format shown on the image signify and how do I plot this on my TI-83 graphing calculator?

2. ## Re: Unfamiliar Cubed Root Function

I can only guess that in their attempt to write the cube root symbol:

the graphic got messed up. But the plot on the graph itself is correct. As for your graphing calculator - recall that taking the cube root of a number is the same as raising it to the 1/3 power, so $\sqrt[3] {x^2}$ is the same as $x^{2/3}$.

3. ## Re: Unfamiliar Cubed Root Function

Originally Posted by ebaines
I can only guess that in their attempt to write the cube root symbol:

the graphic got messed up. But the plot on the graph itself is correct. As for your graphing calculator - recall that taking the cube root of a number is the same as raising it to the 1/3 power, so $\sqrt[3] {x^2}$ is the same as $x^{2/3}$.
Thanks ebaines - I think you are correct. Later in the lesson it showed the limit difference quotient with h approaching zero, except the right arrow was replaced with an ® symbol.

Since it is the same, the $x^{2/3}$ makes perfect sense now.

Thanks!