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

1 Answer
Sep 15, 2015

Answer:

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]}