Question

select the option that best describes the basic shape of the graph of the radical function shown below . F(x) = x^1/6

Answer 1

we are given the function

$y=x^{\frac{1}{6}}$

to picture this graph, we can find the inverse. It would be

$y=x^6$

which looks like this:

now, note that the shape of the function of y=x^1/6 is mostly the same, but rotated to the right. Also, for y=x^1/6 to be a function, we must discard half of the graph. So the graph of the function will look as the half of a parabola turned on its side.