Question

This makes no sense to me so please explain
Find the domain, period, range, and amplitude of the cosine function.

y = -6cos4x

Answer 1

http://www.elmer.unibas.ch/pendulum/sinus.gif

Answer 2

keep in mind that cosine, no matter what it takes as value, will NEVER be > 1 or < -1
so
-1 < cos(WHATEVER) < 1

Answer 3

so any value in front of the function, that is a multiplier will only be able to multiply at the most by 1 or least -1

so the amplitude, that is how high and low over the y-axis cosine will go will be
Acos(x)
or A* 1, or A * -1
so it will go as high as A
and as low as -A
so the amplitude, the distance from the symmetry line will A
-6cos(x) amplitude is, well |-6| = 6

Answer 4

original period for cosine would be \(\bf 2\pi\)
period for cos(\(\color{blue}{B}\)x) will be \(\cfrac{2\pi}{\color{blue}{B}}\)