Question 1097001
<pre>
Solve for y and see if there are more than one value for any x.

{{{(y-2)^3+3}}}{{{""=""}}}{{{x}}}

{{{(y-2)^3}}}{{{""=""}}}{{{x-3}}}

{{{root(3,(y-2)^3)}}}{{{""=""}}}{{{root(3,x-3)}}}

{{{y-2}}}{{{""=""}}}{{{root(3,x-3)}}}

{{{y}}}{{{""=""}}}{{{root(3,x-3) + 2}}}

There is only one real cube root on any number, so 
yes, this is a function.

Here is the graph:

{{{drawing(400,200,-10,6,-2,6,
graph(400,200,-10,6,-2,6,(x-3)^(1/3)+2),

red(line(2.98,1.74,3,1.88),line(3,1.88,3.01,2.24)),
graph(400,200,-10,6,-2,6,-(3-x)^(1/3)+2)

)}}}

The graph of a function is one that never passes under 
or over any part of itself.  This one doesn't.

Edwin</pre>