Question

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

Answer 1

See explanation.

Explanation:

It looks similar to `y = x^(1/3) = root(3)x`.

Here is the graph of `y = x^(1/3) = root(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^(rd)` roots, so all of the `y` values are positive (and have the value of the square.)

`x^(2/3) = (x^(1/3)) = (root(3)x)^2`

Here is the graph of `f(x) = x^(2/3)`

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