Question

What is the range of `y = -2 cos 3x`?

Answer 1

`{yinRR|-2<=y<=2}`

Explanation:

We have to know the range of a normal `cos(x)` function and that is 1 and -1

We next have to know what the translation form of cosine graphs looks like

`Acos[B(x-C)]+D`

A~Amplitude, stretches all the y values by A
B~Period, stretches the period by `1/B`
C~ vertical translation, moves the x values across by C
D~ horizontal translation, moves the y values up D

So A and D effect the range and B and C effect the domain

So from this we know the y values have been stretched by -2 so the range becomes -2 and 2

`{yinRR|-2<=y<=2}`