Question

The number of asymptotes of the curve $y=\frac{7-x^2}{7+x^2}$ is

Answer 1

Given, $y=\frac{7-x^2}{7+x^2}$ Domain is $R$
$\because y$ is defined $\forall x\in R,$ it doesn't have vertical asymptote
Now, $\underset{x\to \pm \infty }{lim}\left(\frac{7-x^2}{7+x^2}\right)=\underset{x\to \pm \infty }{lim}\left(\frac{\frac{7}{x^2}-1}{\frac{7}{x^2}+1}\right)=-1$
$\therefore y=-1$ is the horizontal asymptote.
Given curve doesn't have inclined asymptote
$\{\because \underset{x\to \pm \infty }{lim}\frac{y}{x}=0\}$
Hence it has only $1$ asymptote.