Question

How do you use transformation to graph the cosine function and determine the amplitude and period of `y=cos(x)-6`?

Answer 1

The amplitude of `cos(x)-6` is 1 and the period is `2pi`.

Explanation:

The amplitude of the function, simply put, is the absolute value of the coefficient of `cos(x)`, because that number is quite literally the distance from a crest to the equilibrium, which is also the definition of amplitude. Given that the coefficient is 1, the amplitude is 1.

The period is given by `(2pi)/z` in `cos(zx)`. This is because the coefficient `z` indicates the amount of horizontal compression of the graph. Given that `z=1` in this case, the period is `(2pi)/(1)=2pi`.

P.S. my explanation is very brief, because I forgot quite a lot of the technical terms, but I hope that would do.