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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 $\displaystyle y = \sqrt[3]{x^2} + 1$ 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?

Thanks in advance.

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Re: Unfamiliar Cubed Root Function

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

Attachment 25339

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 $\displaystyle \sqrt[3] {x^2}$ is the same as $\displaystyle x^{2/3}$.

Re: Unfamiliar Cubed Root Function

Quote:

Originally Posted by

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

Attachment 25339
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 $\displaystyle \sqrt[3] {x^2}$ is the same as $\displaystyle x^{2/3}$.

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 $\displaystyle x^{2/3}$ makes perfect sense now.

Thanks!