Question 960959
First thought is you are correct.... Look at the graph:


{{{graph(300,300,-8,4,-8,4,1/x-3)}}}


Critical x values are 1/3  and 0.  Sign changes at x=1/3.


Before graphing, sometimes this helps:


{{{1/x-3x/x}}}


{{{(1-3x)/x}}}


Root when 1-3x=0, and function undefined having vertical asymptote for x=0.