In Problems 14-17, refer to the following graph of y = f(x)

The notation $\underset{x\to a^{+}}{\lim }$ implies the limit calculated by approaching the point $x=a$ from the right. The notation $\underset{x\to a^{-}}{\lim }$ implies the limit calculated by approaching the point $x=a$ from the left. 

If for a function $\underset{x\to \pm \infty }{\lim }f\left(x\right)=a$ the it has the horizontal asymptote $y=a$. If the function tends to $\pm \infty$ as $x\to a$ then the function has a vertical asymptote $x=a$.

From the graph it is clear that function has horizontal asymptote $y=5$ and has a vertical asymptote $x=2$.

14.

Limit to be calculated is $\underset{x\to \infty }{\lim }f\left(x\right)$. From the graph we see that as $x\to \infty$ the function approaches the line $y=5$.

Hence, $\underset{x\to \infty }{\lim }f\left(x\right)=5$.

15.

Limit to be calculated is $\underset{x\to -\infty }{\lim }f\left(x\right)$. From the graph we see that as $x\to -\infty$ the function approaches the line $y=5$.

Hence, $\underset{x\to -\infty }{\lim }f\left(x\right)=5$.