indicate which kind of asymptote it is

Question

For the following functions, use "x" to indicate that the x-axis is an asymptote, "h" to indicate a horizontal asymptote other than the x-axis, "v" to indicate a vertical asymptote, "s" to indicate a slanted asymptote, and "n" the lack of an asymptote. If the graph of a function has several types of asymptotes indicate them all in alphabetical order.

f(x)= x/(x-1)²

f(x)=x²/(x-1)²

f(x)=x³/(x-1)²

f(x)=x²/x²+1

 

Answer 1

f(x)= x/(x-1)^2     x v

f(x)=x^2/(x-1)^2  h v

 

f(x)=x^3/(x-1)^2  v s

f(x)=x^2/x^2+1    h, and there's a hole at x = 0