find all the asymptotes

Question

For the following functions, indicate that the x-axis is an asymptote, a horizontal asymptote other than the x-axis, a vertical asymptote, a slanted asymptote. Indicate as well if there is a lack of an asymptote. Indicate as well if the function has more than one type of asymptote. 

f(x)= 1/x

f(x)=x³/x²-1

f(x)=x³/x²+1

Answer 1

f(x)= 1/x                      x=0 vert., y=0 horiz.

f(x)=x^3/(x^2 - 1)       x=±1 vert., y=x slant.

 

f(x)=x^3/(x^2 + 1)      y=x slant.