discuss the curves under the headings given in this section

Question

y=x/x-1

Answer 1

I assume you mean asymptotes, max/min, etc.

y = x/(x-1)
y' = -1/(x-1)^2
y'' = 2/(x-1)^3

hor. asymptote at y=1 since degree is the same top and bottom. As x gets large, y acts like x/x = 1

vertical asymptotes where denominator is zero

max/min where y' = 0 and y'' not zero
increasing where y' > 0
concave up where y'' > 0
inflections at y'' = 0

Take it awaaaay!