AP Calculus BC : 1.15 Connecting Limits at Infinity and Horizontal Asymptotes- Exam Style questions with Answer- MCQ

Question

Let f be the function defined by \(f(x)=\frac{3x+5}{x+2}\). Which of the following statements are true?

I .The graph of f has a horizontal asymptote at y=3 because .\(\lim_{x\rightarrow \infty }f(x)=3\).
II. The graph of f has a horizontal asymptote at y=3 because \(\lim_{x\rightarrow -\infty }f(x)=3\)
III. The graph of f has a vertical asymptote at x=−2 because \(\lim_{x\rightarrow2^{+}}f(x)=-\infty \).
A I only
B III only
C I and II only
D I, II, and III