please help me. How do I solve this: Given the function f(X) = 5 sin (-2x + 540^o) - 4

Question

1. State the transformations
2. Show your transformation statement and table of values
3. State the domain and range of the function
4. Graph 2 cycles of the function

Answer 1

5sin(-2x + 540) - 4

= 5sin(-2x + 3pi) - 4

range is -9 to 1, -4-5 to -4+5

-9< f(x) < 1

mid line is y=-4 = average y value, -9+1)/2 =-8/2 = -4

domain is any real number

parent function is f(x) = sinx

It's stretched vertically by a factor of 5

shifted vertically down by 4

shifted horizontally left by 540 degrees

reflected across the y axis

with the period compressed from 2pi to 2pi/-2 = -pi

general form of the sine function

is f(x) = Asin(Bx +C) + D

where A is the vertical stretch, = 5

D is the vertical shift =-4

C is the horizontal shift = 3pi/2

period = 2pi/B = 2pi/-2