Does the function "y=abs(x)" have a horizontal asymptote? ?

Question

I know that it literally touches the x-axis at (0,0), so I'm guessing that the x-axis is not its horizontal asymptote. However, I'm not sure? Is the x-axis (y=0) the horizontal asymptote? THANK YOU in advance to whoever can help me with this problem. I really appreciate it :]

Answer 1

If it has an asymptote y=a, then it will never be defined there. the absolute value function is always defined, so no, there is no asymptote, vertical or horizontal.

Answer 2

No it doesn't.

A horizontal asymptote is basically just the limit of the function as x goes  to infinity.

Answer 3

You are right! There is no horizontal asymptote for the equation y=abs(x). A horizontal asymptote occurs only if as x becomes very large (or very small) and the graph approaches some horizontal line. Since the graph tends to grow infinitely, this means that the graph is NOT approaching any horizontal line.

Note: the graph can cross its horizontal asymptote (but not its vertical asymptote). So it's possible for a graph with a horizontal asymptote to have a value defined on the asymptote itself. For instance the graph y=(x^2)/(x^3+2x) has a horizontal asymptote y=0 and it has the point (0,0) defined on the graph (notice how the point is on the horizontal asymptote).