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?
b) Determine f(x) and f(x). Determine all horizontal and vertical asymptotes of the function.
I got that lim x-->inf it goes to inf and lim x-->-inf goes to -inf.
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.
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.
x __|- | + | +
x-2 |- | - | +
f '_ |+ | - | +
___up, down, up. so there must be a maximum at 0 and a minimum and 2. right?