Shifting graphs up down left right?

Question

I need someone to tell me if I am doing this right please.

With the equation 0.5cos 4x Shifting it up by 3 would make the equation look like:

0.5cos 4x +3? Shifting left by pie would look like:

0.5cos (4x(x+pie))?

3 times the amplitude, half the period, shift Pie right:

1.5cos (8x(x-pie))?

The graphs look like:

http://education.yahoo.com/homework_help/math_help/solutionimages/miniprecalcgt/6/1/1/miniprecalcgt_6_1_1_8_50/f-460-26-ex-1.gif

Answer 1

Shifting it up by 3 would make the equation look like:

0.5cos 4x +3?  Correct, but I would write it 3 + 0.5cos(4x)

Shifting left by π would look like:

0.5cos (4x(x+π))? should be 0.5cos(4x+π)

3 times the amplitude, half the period, shift π right:

1.5cos(8x - π)