# What is the graph of f(x)=x^(2/3)?

Sep 15, 2015

See explanation.

#### Explanation:

It looks similar to $y = {x}^{\frac{1}{3}} = \sqrt[3]{x}$.

Here is the graph of $y = {x}^{\frac{1}{3}} = \sqrt[3]{x}$.

graph{y = x^(1/3) [-3.08, 3.08, -1.538, 1.54]}

You can scroll in and out and drag the graph window around using a mouse.

The difference is that the function in this question has squared all of the ${3}^{r d}$ roots, so all of the $y$ values are positive (and have the value of the square.)

${x}^{\frac{2}{3}} = \left({x}^{\frac{1}{3}}\right) = {\left(\sqrt[3]{x}\right)}^{2}$

Here is the graph of $f \left(x\right) = {x}^{\frac{2}{3}}$

graph{y = x^(2/3) [-3.08, 3.08, -1.538, 1.54]}