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HW and Stamp Sheet out on your desk!!

HW and Stamp Sheet out on your desk!!. 4.6 Phase Shifts. Recall from yesterday:. y = asin ( tx ) y = acos ( tx ). Amplitude of the graph = a Period of the graph =. Phase Shift (h). y = asin ( tx - h) y = acos ( tx - h).

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HW and Stamp Sheet out on your desk!!

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  1. HW and Stamp Sheet out on your desk!!

  2. 4.6 Phase Shifts

  3. Recall from yesterday: y = asin(tx) y = acos(tx) Amplitude of the graph = a Period of the graph =

  4. Phase Shift (h) y = asin(tx - h) y = acos(tx - h) When a graph shifts left or right, it is called a phase shift. h tells us the direction and how far to shift. Note that h is subtracted, so go the opposite direction that you would assume.

  5. Example 1: State the direction and distance that each function has shifted. 1. y = sin(x + π) 2. y = cos(x – ) 3. y = cos(x + ) 4. y = sin(x – )

  6. Vertical Shift (k) y = asin(tx - h) + k y = acos(tx - h) + k When a graph moves up or down, it is called a vertical shift. k tells us which direction and how far to shift.

  7. Example 2: State the direction and distance that each function has shifted. • y = cos(x-π) – 3 • y = sin(x+2π) – 2 • y = sin(x-4π) + 4 • y = cos(x-1) + ½

  8. Putting it all together! y = asin(tx - h) + k y = acos(tx - h) + k Amplitude of the graph = a Period of the graph = Horizontal translation = h (note: opposite direction) Vertical translation = k

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