Finding the period of a function?

**iluvmathbutitshard** · November 9th 2009, 08:29 AM

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?

**skeeter** · November 9th 2009, 08:39 AM

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?

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

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

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.

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