## rosedewittbukater 2 years ago Help please? Write a rational function with no vertical asymptotes and no holes. Explain. I was thinking x/x^2+1 but I can't tell if it has a vertical asymptote.

1. getusel

yes you are absolutely right

2. rosedewittbukater

@getusel How can I know is there's an asymptote? Those confuse me.

3. getusel

find the roots of the denominator

4. rosedewittbukater

Also I thought it doesn't have any zeros, but now I'm thinking it might.

5. getusel

if the denominator of the rational expression has a solution, it has asymptotes.if not it does not have one.

6. getusel

the roots should be real number

7. rosedewittbukater

Does this denominator have one?

8. getusel

it does not have a real solution for the denominator. This implies that it does not have any.

9. rosedewittbukater

How would I know if it had a vertical asymptote? Something about when you find the zeros, it can't have a common zero with the nominator. I don't think the function can be factored any more so would this be the right answer?

10. rosedewittbukater

Did I just say nominator? I meant numerator lol.