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?
$\displaystyle y = \frac{1}{2}\sec\left(\frac{\pi}{2} \cdot x\right)$
$\displaystyle y = \frac{1}{2\cos\left(\frac{\pi}{2} \cdot x\right)}
$
period, $\displaystyle T = \frac{2\pi}{B} = \frac{2\pi}{\frac{\pi}{2}} = 4$
asymptotes will be the values of x that make $\displaystyle \cos\left(\frac{\pi}{2} \cdot x\right) = 0$ ... that should be rather easy to determine.