Question

find the horizontal and vertical asymptotes with the domain of f(x)= 4/x^2

Answer 1

x≠0 so the line x=0 is an asymptote,
y≠0 so the line y=0 is also an asymptote,
these lines are the the y,x axises

Answer 2

If x = 0 the function is undefined so the y axis is a vertical asymptote. A positive number divided by a positive number will always be positive so y is always positive so the x axis is a horizontal asymptote. The domain is all real numbers except 0 and the range is all positive real numbers.