# For what values of x, if any, does f(x) = secpix  have vertical asymptotes?

Jul 7, 2016

$x = \frac{\left(2 k + 1\right)}{2} , q \quad k \in m a t h b f \left(Z\right)$

#### Explanation:

for vertical asymptotes we look for a denominator of 0

here we have

$f = \sec \pi x = \frac{1}{\cos \pi x}$

the denom will be zero at
$\pi x = \frac{\pi}{2} , \frac{3 \pi}{2} , \ldots . , \frac{\left(2 k + 1\right) \pi}{2} , q \quad k \in m a t h b f \left(Z\right)$

ie
$x = \frac{\left(2 k + 1\right)}{2} , q \quad k \in m a t h b f \left(Z\right)$