Question 887652
This is not a complete answer, but some help about {{{g(x)=sqrt(x-3)/(5-x)}}}.


In real numbers, {{{x>=3}}} is necessary.  As x tends to 3 from the right, g becomes increasingly negative, <s>and this seems to be an asymptote</s>  there is a horizontal axis intercept for x=3.  Also a critical point occurs at x=5; in that for g to be defined, {{{x<>5}}}.


More theoretical stuff can be done, but....


{{{graph(300,300,-3,12,-3,12,sqrt(x-3)/(5-x))}}}