FINDING AMPLITUDE PERIOD PHASE SHIFT AND VERTICAL SHIFT WORKSHEET

Determine the amplitude, period, phase shift and vertical shift for each.

Problem 1 :

Problem 2 :

Problem 3 :

Problem 4 :

Determine the amplitude, period, phase shift and vertical shift of the function. Then graph one period of the function.

Problem 5 :

Problem 6 :

Answer Key

Amplitude = 3,

Period = 𝜋/2

Moving the graph towards left of 𝜋/8

Moving the graph 2 units up.

Amplitude = 1/2

Period = 𝜋

Then there is no phase shift.

Moving the graph 4 units down

Amplitude = 2

Period = 2𝜋

Horizontally move the graph right 𝜋.

There is no vertical shift.

Amplitude = 4

Period = 2𝜋

Horizontally move the graph right 𝜋.

Move the graph down 3 units.

Amplitude = 1

Period = 2𝜋

Horizontally move the graph right 𝜋/2.

There is no vertical shift.

So, the points are (𝜋/2, 1) (𝜋, 0) (3𝜋/2, -1) (2𝜋, 0). Plotting the points and joining the points.

Amplitude = 4

Period = 𝜋

Horizontally move the graph right 𝜋/3.

There is no vertical shift.

the points are (𝜋/3, 0) (7𝜋/12, 4) (5𝜋/6, 0) (13𝜋/12, -4) (4𝜋/3, 0). Plotting the points and joining the points.