# Finding the period of a function?

• November 9th 2009, 08:29 AM
iluvmathbutitshard
Finding the period of a function?
Ok, so my assignment is to match a function with its graph. The function given is y = 1/2 sec (pi x)/(2).
So, to identify which graph matches, I would have to find the period and 2 asymptotes.

How would I do this?
• November 9th 2009, 08:39 AM
skeeter
Quote:

Originally Posted by iluvmathbutitshard
Ok, so my assignment is to match a function with its graph. The function given is y = 1/2 sec (pi x)/(2).
So, to identify which graph matches, I would have to find the period and 2 asymptotes.

How would I do this?

$y = \frac{1}{2}\sec\left(\frac{\pi}{2} \cdot x\right)$

$y = \frac{1}{2\cos\left(\frac{\pi}{2} \cdot x\right)}
$

period, $T = \frac{2\pi}{B} = \frac{2\pi}{\frac{\pi}{2}} = 4$

asymptotes will be the values of x that make $\cos\left(\frac{\pi}{2} \cdot x\right) = 0$ ... that should be rather easy to determine.