Answer
a) $\lim\limits_{x\to \infty} =3$
and $\lim\limits_{x\to -\infty} =-2$
b) $y=3$ and $y=-2$
Work Step by Step
a) From the graph it can be seen that $\lim\limits_{x\to \infty} =3$
and $\lim\limits_{x\to -\infty} =-2$
b) Let us consider that the function $f(x)$ is defined om some interval $(a, \infty)$.
Then , we have $\lim\limits_{n\to \infty} f(x)=L$
This implies that the value of the function $f(x)$ can be defined arbitrarily close to the limit $L$ by taking $x$ sufficiently large.
Then, the line $y=L$ is called a horizontal asymptote of the function $y=f(x)$
The equations of horizontal asymptotes are:
$y=3$ and $y=-2$
