# Thread: What's the domain of a func. with repeating vertical asymptotes in interval notation?

1. ## What's the domain of a func. with repeating vertical asymptotes in interval notation?

Would infinite unions be used? How would it apply to f(x) = sec(x)?

2. Originally Posted by essaymasters
Would infinite unions be used? How would it apply to f(x) = sec(x)?
see the attached graph for y = sec x

Domain = $\{ x \in \mathbb {R} ,\;x \ne \frac{(2n-1)\pi}{2} \}, \;n \in \mathbb {I}, \; integer$

3. Thanks Shyam! One more question though, how would this intersect with $g(x) = \frac{1}{(x-7)(x+2)}$?

4. Originally Posted by essaymasters
Thanks Shyam! One more question though, how would this intersect with $g(x) = \frac{1}{(x-7)(x+2)}$?
For, $g(x) = \frac{1}{(x-7)(x+2)}$, the vertical asymptote are at x= 7 and x = -2 and horizontal asymptote y = 0 (x-axis is horizontal asymptote)