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

• Jan 7th 2009, 06:15 PM
essaymasters
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)?
• Jan 7th 2009, 06:39 PM
Shyam
Quote:

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 = $\displaystyle \{ x \in \mathbb {R} ,\;x \ne \frac{(2n-1)\pi}{2} \}, \;n \in \mathbb {I}, \; integer$
• Jan 7th 2009, 06:57 PM
essaymasters
Thanks Shyam! One more question though, how would this intersect with $\displaystyle g(x) = \frac{1}{(x-7)(x+2)}$?
• Jan 7th 2009, 07:06 PM
Shyam
Quote:

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

For, $\displaystyle g(x) = \frac{1}{(x-7)(x+2)}$, the vertical asymptote are at x= 7 and x = -2 and horizontal asymptote y = 0 (x-axis is horizontal asymptote)