Determine the amplitude, range, period, and phase shift and then sketch the graph of the function using the quarter points. y--2sim (-2x+5)-3 = Which of the following functions is equivalent to y = - 2 sin -2 sin (-2x+3)-37 (x - 17 ) - 3 O A. y 4 sin x OC. y=-2 sin 2x- π O B. y=-2 sin 2 sin (2x + 3) +3 O D. y=2 sin 2x--

List the transformations made to the cosine function and write an equation of the form Y= A cos[B(x - C)] + D whose graph is the given cosine function below. Also state the range.

1. -5TT/4 -8 -7- 6 5 WW -2 -3/4 -TT/2 -TT/4 0 -1- TT/4 Give the midline (vertical shift) of the function. d. Give the amplitude of the function. Amplitude = 3 TT/2 + a. On the graph shown, highlight one period of the function. b. Give the period of this function. 3TT/4 e. Find an equation for this graph of the form f(x)= a sin(b(x−c))+d (Bonus points if you can give more than one answer!) 3sin( f. Find an equation for this graph of the form f(x) = a cos(b(x-c))+d 577/4

Compare the phase shift and amplitude of y=-cos(x-180∘) and y=-2sin(x-90∘). Which of the following choices is the correct comparison? a The cosine function has a phase shift that is 12 that of the sine function and in the same direction; the amplitude of the cosine function is 2 times that of the sine function. b The cosine function has a phase shift that is 12 that of the sine function and in the opposite direction; the amplitude of the cosine function is 12 that of the sine function. c The cosine function has a phase shift that is 2 times larger than the phase shift of the sine function and in the same direction; the amplitude of the cosine function is 12 that of the sine function. d The cosine function has a phase shift that is 2 times larger than that of the sine function and in the opposite direction; the amplitude of the cosine function is 2 times that of the sine function.