State the amplitude, period, phase shift, and vertical shift of f(x) = −2 sin( x+1 /4 ) − 3

Answer 1

You want to make sure the function is written in "standard transformation format" before determine the answers to your question. Standard transformation format for a sine or cosine is y = Asin[B(x - C)] + D

where A is the amplitude; B is used to find the period - the period is 2π/B; C is the phase shift and D is the vertical shift.

In this case, A = 2 (ignore the negative); B = 1; C = -1/4; and D = -3

So the amplitude is 2.

The period is 2π/1 = 2π.

The phase shift is -1/4

The vertical shift is -3.