Question

Which statement about the function f(x)=x(x – 3)(x – 2) is true?

It has no horizontal asymptote.


It does not cross the horizontal asymptote.


It crosses the horizontal asymptote at the origin.


It has one vertical asymptote.

Answer 1

C,

It crosses the horizontal asymptote at the origin.

Explanation:

Plato

Answer 2

It has no horizontal asymptote

Explanation:

It has no horizontal asymptote. This is a cubic function which has the end behavior of the left tail down and the right tail up, so both the domain and the range are infinity. That means that there is no horizontal asymptote to go through. Because it is not a rational function, there are no vertical asymptotes that could make the denominator go to 0 since there is no denominator (not rational).