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

1 Answer
Jan 7, 2018

Answer:

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.