Question

Which statement is true

Answer 1

Since the degree of numerator and denominator is the same, the horizontal asymptote will be equal to the ratio of coefficient of leading terms.

So, horizontal asymptote for given expression will be y = 3

Vertical asymptote occurs where denominator is zero. So the given expression will have vertical asymptotes at x=2 and x=-2

Thus, there are two vertical asymptotes and one horizontal asymptote.

Therefore, the correct option is Fourth Option

Answer 2

The true statement is: The graph has tow vertical asymptotes and one horizontal asymptote.

We can see in the graph that the vertical asymptotes are $x=2$ and $x=-2$, so the first statement is false.

We can also check that the horizontal asymptote is $y=3$, so the second statement is false as well.

A graph of a function never crosses its asymptotes, so the third statement is false.

We can conclude that the correct answer is: The graph has tow vertical asymptotes and one horizontal asymptote.