# Graphs of functions with fractional powers: $x^{p/q}$

How does changing the value of $\dfrac{p}{q}$ affect the drawing of the graph (domain/range/shape, etc.) How do you calculate asymptotes?

Below is a question dealing with this type of function. Can someone please refer to the explanations on how to go about solving these questions? I have no idea because I don't understand these graphs

• Do you know $\sqrt[m]{A^n}=A^{n/m}$? Jan 4 '14 at 2:52
• yes :) i know this. Jan 4 '14 at 2:54

The graph of $y=\sqrt[m]{(x-a)^n}$ is a graph such that the graph of $y=\sqrt[m]{x^n}$ is parallel-shifted by $a$ in the $x$ direction.
Since $y=f(x)$ has a maximal domain of $[-a, \infty)$...
• $x^{1/3}$ and $x^{2/3}$ has the domain $x\in\mathbb R.$ But your function does not have the domain $x\in\mathbb R.$ This means that your function is not in the form of $(x\pm a)^{1/3}, (x\pm a)^{2/3}.$ Jan 4 '14 at 3:45