1. For each of the given functions, determine the amplitude or vertical stretching/shrinking, period, phase shift, and vertical shift. (4 points each)
1. y = -2sinx - 5
2. y = tan2(x - p/4) + 1
3. y = sec0.5x + 2
4. y = 0.5cos1.5(x - p)
5. y = -4csc(2x + p)
6. y = 3cotx
2. For each of the given graphs, determine the amplitude, period, and vertical shift. Then state the equation of the function. (4 points each)
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2.
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4.
3. Graph each function using the given interval. (6 points each)
1. y = 2sinx + 1, [-2p, 2p]
2. y = sec2x, [0, 2p]
3. y = -2cosx, [0, 2p]
4. y = sin2x - 2cosx, [0, 2p]
5. y = -3cos0.5x, [0, 4p]
6. y = -2sin(x - p/2), [0, 4p]
7. y = cos(x + p) - 2, [0, 4p]
8. y = tanx + 1, [-2p, 2p]
9. y = 2cscx, [-2p, 2p]
10. y = cosx + 2sinx, [0, 2p]
1. For each of the given functions, determine the amplitude, period, phase shift, and vertical shift. (4 points each)
1. amp = 2, pd = 2p, ps = 0, vs = 5 down
2. none, pd = p/2, ps = p/4 right, vs = 1 up
3. amp = 1, pd = 4p, ps = 0, vs = 2 up
4. amp = 0.5, pd = 4p/3, ps = p right, vs = 0
5. (First factor out 2: y = -4csc2(x + p/2)) amp = 4, pd = p, ps = p/2 left, vs = 0
6. v. stretch = 3, pd = p, ps = 0, vs = 0
2. For each of the given graphs, determine the amplitude, period, and vertical shift. Then state the equation of the function. (4 points each)
1. amp = 0.5, pd = 2p, vs = 0, y = -0.5sinx
2. amp = 1, pd = p, vs = 0, y = cos2x
3. amp = 1, pd = 2p, vs = 2 down, y = sin0.5x - 2
4. amp = 2, pd = 2p, vs = 1 up, y = 2cosx + 1
3. Graph each function using the given interval. (6 points each)
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2.
3.
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