Question 912238
f(x)=x/(x^2-7x)
f(x)=x/(x(x-7))
Critical x values are 0 and 7.


No vertical root for x at zero because x is both in the numerator AND the denominator.
f is undefined and discontinuous for x at 0.


Vertical asymptote at x=7 because undefined for x at 7.


Intervals of x<0, 0<x<7, 7<x.
Near x=0, f <s>becomes increasingly</s> negative from either direction. (?)


Within 0<x<7,
f=(+)/((+)(-))
f is negative


Within 7<x,
f=(+)/((+)(+))
f is positive


That analysis is not really complete, but this should be the graph:


{{{graph(300,300,-10,10,-10,10,x/(x^2-7x))}}}