Question

Identify the horizontal and vertical asymptotes, if any, for the graph of f(x) shown. Check all that apply.

y = 0
y = 1
x = 1
x = –1
no vertical asymptotes
no horizontal asymptotes

Answer 1

I don’t see the graph — could you upload it or describe its behavior? To identify which of the listed lines are asymptotes, check these things:

- Horizontal asymptote y = c: does f(x) approach the constant c as x → +∞ and/or x → −∞? If it does for either/both ends, mark that horizontal asymptote. (You can have different horizontal limits at +∞ and −∞.)

- Vertical asymptote x = a: does f(x) blow up to ±∞ as x approaches a from the left or right? If yes, x = a is a vertical asymptote.

Using the choices given:
- If the graph levels off to the x-axis on the far left or right, select y = 0.
- If it levels off to height 1 on the far left or right, select y = 1.
- If the graph shoots to ±∞ near x = 1, select x = 1.
- If it shoots to ±∞ near x = −1, select x = −1.
- If it never blows up near any finite x, select no vertical asymptotes.
- If it doesn’t approach any finite constant as x → ±∞, select no horizontal asymptotes.

Send the image or describe the end-behavior and any blow-ups near x = 1 or x = −1 and I’ll pick the correct options.