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

Answer 1

For a function of the form y = Asin(Bx+C) + D, amplitude = lAl, period = 2π/ lBl, phase shift = -C/B, and vertical shift = lDl.

So, for y = -2sin(x + 1/4) - 3, amplitude = 2, period = 2π/1 = 2π, phase shift = -(1/4)/1 = -1/4 (meaning 1/4 unit to the left), and vertical shift = 3 units downward.