Question

What are the two invisible lines are and how to predict them when graphing a function

Answer 1

They don't have to be invisible; you could graph them if you like. We're talking about vertical and horizontal asymptotes. Please look that up in your text.

Vertical asymptotes apply primarily to rational functions. Set the denominator == to zero and solve for any real roots. Write the results as equations; these are your equations of the vertical asymptote or asymptotes. For example: x = 3.

Answer 2

Thank you! And well in the question they stated them as invisible lines.

Answer 3

Horiz. asymptotes are usually fairly easy to find. They correspond to "behavior at infinity," what happens to the function as x becomes large without bound. Try your textbook for some examples. Good luck!

Answer 4

The horizontal asymptote is usually on the x-axis. You can cross these more than you could with a vertical asymptotes. A horizontal asymptote tells you where the graph would go on an x-axis if it's pretty big.


if this a good description?

Answer 5

Actually, StillFly, horizontal asymptotes are on or parallel to the x-axis. A horizontal asymptote gives you a picture of the limiting behavior of a given function as x increases without bound (or becomes increasingly large). Only very occasionally does a graph cross its horizontal asymptote.

Answer 6

Oh, thank you. Sorry I read somewhere where it said completely the opposite!