Question

Give the equation of the graph of y = 2 cos 3x + 1 after it has been stretched vertically by a factor of 2, flipped upside down, and stretched horizontally by a factor of 2.

Answer 1

Explanation:

So we have the following chain of transformations

`f(x)\to 2f(x)\to -2\f(x)\to -2f((1)/(2)x)\\`

So now

`-2f((1)/(2)x)=-2\left(2\cos(3x/2)+1\right)=-4\cos(3x/2)-2`