Unit 4 Test Review Part 1 – Critical Points
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Curve:
Amp.
Pd.
1
y = 1 – sin x
1
2
y = 2 + 2sin(x + 45°)
3
4
Name:____________________________________ Date:___________________Period:_______
Critical Points (in degrees)
Vertical
Trans.
Range
Shape
Vertical
Stretch
Horizontal
Stretch
2π
Phase
Shift &
Direction
______
0, 90, 180, 270, 360
Up 1
[ 0 , 2]
Stretched
Shrunk
2
2π
45° left
-45, 45, 135, 225, 315
Up 2
[ 0 , 4]
y = -2 – cos(3x + 150°)
1
2π/3
50° left
-50, -20, 10, 40, 70
Dn 2
[ -3 ,-1 ]
y = 1 -3cos (1/2) x
3
4π
_______
0, 180, 360, 540, 720
Up 1
[ -2 , 4 ]
Normal
Reversed
Normal
Reversed
Normal
Reversed
Normal
Reversed
Normal
Reversed
Normal
Reversed
Normal
Reversed
Normal
Reversed
Normal
Reversed
Normal
Reversed
Normal
Reversed
Normal
Reversed
Compressed
Elongated
Compressed
Elongated
Compressed
Elongated
Compressed
Elongated
Compressed
Elongated
Compressed
Elongated
Compressed
Elongated
Compressed
Elongated
Compressed
Elongated
Compressed
Elongated
Compressed
Elongated
Compressed
Elongated
5
y = -1/2 sin (x - 60°)
1/2
2π
60° right
60, 150, 240, 330, 420
______
[ -1/2,1/2]
6
y = -2 + sin (2/3x + 90°)
1
3π
135° left
-135, 0, 135, 270, 405
Dn 2
[-3,-1]
7
y = 3 + cos(2x – π/2)
1
π
π/4 right
45, 90, 135, 180, 225
Up 3
[ 2 , 4]
8
y = -1 – 2cos(3x + π/3)
2
2 π/3
-20, 10, 40, 70, 100
Dn 1
[-3, 1]
9
y = 2 + cos (3/2x - 30°)
1
4 π/3
π/9 or 20°
left
20° right
20, 80, 140, 200, 260
Up 2
[1, 3]
10 y = 1 + sin(2/3x + π/2)
1
3π
135° left
-135, 0, 135, 270, 405
Up 1
[0, 2 ]
11 y = -2 – 2 sin5(x + 45°)
2
2 π/5
45° left
-45, -27, -9, 9, 27
Dn 2
[ -4 ,0]
12 y = 3 + ½ cos3(x + π/6)
1/2
2 π/3
30° left
-30, 0, 30, 60, 90
Up 3
[2.5,3.5]
Stretched
Shrunk
Stretched
Shrunk
Stretched
Shrunk
Stretched
Shrunk
Stretched
Shrunk
Stretched
Shrunk
Stretched
Shrunk
Stretched
Shrunk
Stretched
Shrunk
Stretched
Shrunk
Stretched
Shrunk