Hey guys, please tell me if I'm correct in my calculations

Given the function

a) Determine the domain and all the intercepts of the function. Does the function have any symmetry?

This is what I did: Domain is all real #s except 1, because x-1=0, x=1.

intercepts are/is: (0,0) because =0

it's symmetric because =

Is this right?

I got that lim x-->inf it goes to inf and lim x-->-inf goes to -inf.

b) Determinef(x)andf(x).Determine all horizontal and vertical asymptotes of the function.

Vertical asymptote is 1 as shown above.

Can someone show me how you get the horizontal asymptote for this please?

c) find all critical numbers.Quotient rule:

critical numbers are 0 and 2

d) Determine the intervals on which the function is increasing and where it is decreasing. Find all maximum and minimum values of f.I use a chart.

______0__2

x __|- | + | +

x-2 |- | - | +

f '_ |+ | - | +

___up, down, up. so there must be a maximum at 0 and a minimum and 2. right?