# Horizontal asymptote:can be touched or not?

1. Oct 25, 2015

### gracy

2. Oct 25, 2015

### andrewkirk

Here is a picture of a horizontal asymptote that is crossed. The function is $f(x)=e^{-x}(0.5+e^{-x}\sin 10x)$. The curve crosses the asymptote in both directions, then remains above it as it approaches from above.

3. Oct 25, 2015

### andrewkirk

4. Oct 25, 2015

### gracy

5. Oct 25, 2015

### andrewkirk

You asked whether a horizontal asymptote can be crossed. Above is a graph of a function that crosses its horizontal asymptote.

6. Oct 27, 2015

### Staff: Mentor

You didn't read the above carefully enough. It also says this (emphasis added):
Horizontal asymptotes describe the behavior of a graph for large or very negative values of the dependent variable.