Question

Give an example of a rational function that has a horizontal asymptote at y = 0 and a vertical asymptote at

x = 2 and x = 1.

Answer 1

x/(x-2)(x-1)

Step-by-step explanation: if m<n then horizontal asymptote is y=0

in the function x/(x-2)(x-1) m is bigger then n so y=0

after calculating the vertical asymptote we got x=2 and x=1

hope it helps

Answer 2

f(x)=x^2/(x-2)(x-1), the degree of the numerator and the degree of the denominator equal and the quotient of their coefficient equal to 1(horizontal asymptote means that the lines approach a certain number when the input approaches positive or negative infinity)
and when plugging in 2 or 1 as input, the output is undefined.