Science:Math Exam Resources/Courses/MATH110/April 2018/Question 02 (c)/Solution 1

Since $f$ satisfies ${\textstyle \lim _{x\to 0^{+}}f(x)=+\infty }$, it has a vertical asymptote at $x=0$. On the other hand, the condition ${\textstyle \lim _{x\to +\infty }f(x)=2}$ gives a horizontal asymptote.

One example of such a function is ${\textstyle y=2+1/x}$, which is sketched in the following picture.