# How do you find the amplitude and period of a function y=-3sec(-6x)+2?

Feb 13, 2018

No amplitude for $\sec x$, period=$\frac{\pi}{3}$

#### Explanation:

Our function is in the form $a \sec \left(b x - c\right) + d$. Look at the graph of $\sec x$ below. What do you notice?:

Technically, the graph of $\sec x$ has no maximum or minimum value, therefore there is no amplitude.

The period, however, can be determined using our formula:

$\frac{2 \pi}{|} b |$

In this case, b is the coefficient on our x-term, which is $- 6$. We have to take the absolute value of it, which will make it a positive $6$.

$\frac{2 \pi}{6}$, which can be simplified to $\frac{\pi}{3}$