Question

find vertical/horizontal asymptotes
local extrema

Answer 1

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

Answer 2

vertical asymp is when you factor the denominator, eliminate holes (common terms top and bottom) and whats left makes the bottom=0.

top: 3
bottom: (x-1)^2 = (x-1)(x-1)

Nothing cancels top to bottom so there are no holes. when x=1; the bottom= 0; so x=1 is a vertical asymp.

horizontal asymp is easier to find when top and bottom are not factored, and in this case we get 3/x^2. As x grows very big; this fraction gets closer to 0. The HA is at y=0.