Question

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

Answer 1

No amplitude for `secx`, period=`(pi)/3`

Explanation:

Our function is in the form `asec(bx-c)+d`. Look at the graph of `secx` below. What do you notice?:

Technically, the graph of `secx` has no maximum or minimum value, therefore there is no amplitude.

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

`(2pi)/|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`.

`(2pi)/6`, which can be simplified to `(pi)/3`

Additionally, you can find more info on amplitude, period and phase shift on the site below:
https://www.mathway.com/popular-problems/Precalculus/401080