Give an example of a rational function that has no horizontal asymptote and a vertical asymptote at x = 1.
Example for horizontal asymptote that has none.
x+2
-------
x^2+9+3
Example of a vertical asymptote at x=1
(x-2)(x+3)
------
x-1
no horizontal asymptote does not mean asymptote is \(y=0\) it means it doesn't have one
so from before that means the degree of the numerator is larger than the degree of the denominator
therefore unfortunately your answer is not correct.
you have to make the degree of the top bigger than the degree of the bottom
i can give you an example if you like
not two different functions, one with no horizontal asymptote, and a different one with a vertical asymptote at \(x=1\)
you are correct to put the \(x-1\) in the denominator