Answer
>No. The graph of y=f(x) cannot intersect its vertical asymptote.
> Yes. The graph of y=f(x) can intersect its horizontal asymptote.
>The graph of y = f(x) can only have 2 or less than 2 horizontal asymptotes.
Work Step by Step
a)Vertical Asymptote
As x → c, y → ± ∞,
The value x = c is not in the domain of the function f(x).
Hence, the graph of y=f(x) cannot intersect its vertical asymptote.
Horizontal Asymptote
As x → ± ∞, y → b,
Hence, the graph of y=f(x) can intersect its horizontal asymptote.
b) The graph of y = f(x) can only have 2 or less than 2 horizontal asymptotes.
This is because horizontal asymptotes exists if it satisfies either or both lim x->∞ f(x) and lim x-> -∞ f(x).
