Question

How do you use transformation to graph the cosine function and determine the amplitude and period of `y=-4cos(-3x)`?

Answer 1

As cosine is an even function we have that `cos(-x) = cosx`

so, `cos(-3x) = cos(3x)`

Hence, `y = -4cos(-3x) = -4cos(3x)`

If we start with the graph of `y = cosx`, we need to apply a horizontal squash factor of `1/3` to get `y = cos(3x)`

i.e. the period changes from 360 degrees to 120 degrees

From `y = cos(3x) to y = -4cos(3x)` we apply a stretch factor of 4 parallel to the y-axis and reflect about the x-axis due to the -4

The amplitude is 4.

See the graph below:

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