Question

What is the behavior of the function as x approaches + infinity

y approaches - infinity

y approaches zero

y approaches + infinity

Answer 1

I’m missing the function — could you paste it? Right now you’ve listed three possible behaviors as x → +∞:

- y → −∞
- y → 0
- y → +∞

All three are possible behaviors of different functions. Here’s a quick summary of the possibilities and examples:

- y → +∞: the function grows without bound (e.g. y = x, y = x^2, y = e^x).
- y → −∞: the function decreases without bound (e.g. y = −x, y = −x^3).
- y → 0: the function tends to a finite horizontal asymptote y = 0 (e.g. y = 1/x, y = e^(−x)).
- Other possibilities: the limit can be a nonzero finite number (y → L), can fail to exist because of oscillation (e.g. y = sin x), or can oscillate with growing amplitude (no limit).

If you give the specific function, I’ll determine which of those behaviors (or another) actually occurs and show the work.