Question

If x is continuous for all x, the maximum number of horizontal asymptotes that the graph of f can have is 0, 1, 2, or 3?

Answer 1

2.
Good explain:\[y = \tan^{-1} x\]

Answer 2

Horizontal asymptotes represent long-term behavior, i.e. what happens as x approaches infinity or negative infinity. How many possibilities does that give you?