Question

let f(x)= 9(x/(x-1)square)= 9x/ x square-2x+1
find the domain of f and compute the limit at each of its endpoint. then list all horizontal and vertical asymptotes

Answer 1

f(x) = 9x/(x-1)²)

The domain is all real numbers except where the denominator is zero.

The denominator is zero when x = 1.

There are no endpoints to the domain.

Vertical asymptotes occur when the denominator is zero and numerator is not zero. In other words, the line x=1.

Horizontal asymptotes occur when y approaches a fixed value as x gets large. Note that for huge values of x, f(x) is just 9x/x²

So, as x gets huge y gets closer and closer to zero. The horizontal asymptote is the line y=0.