fill out the information for the following function

Question

f(x)=1/2sin(pi/5(x+6))-2

phase shift:

vertical shift:

amplitude:

period:

Answer 1

Here is the general case:

f(x) = a·sin(b(x-c)) + d

1. a = amplitude
2. b = 2π/period
3. c = phase (horizontal) shift
4. d = vertical shift (moves midline up or down)

If you can remember the general case, you can solve all of these on your own. In your case, we have

f(x) = 1/2·sin(π/5(x+6) - 2:

1. a is the amplitude = 1/2
2. b is π/5 = 2π/period. Solve for the period.
3. c = phase shift = -6
4. d = vertical shift = -2 (midline moves down 2)

Answer 2

f(x) = A sin (B(x + C) + D

amplitude: A

period: 2π / B

phase shift: C (positive to left)

vertical: D

Use this for cosine also.