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y = 2 sin x

A

B

1
y = 3cos ( x + 90° ) − 1
2

C

D

E

1
y = sin ( x + 60° )
2

F

G

H

y = cos x + 2

y = −3sin 2x

y = −2 cos 3( x − 60° )

y = cos 2x − 3

y = sin 3( x − 90° ) + 1
1

2

3

4

5

6

7

8
i

amplitude: 1
period: 360°
maximum: 3
minimum: 1
range: 1 ≤ y ≤ 3
vertical translation: up 2

ii

amplitude: 1
period: 180°
maximum: -2
minimum: -4
range: -4 ≤ y ≤ −2
vertical translation: down 3

1
2
period: 360°
1
maximum:
2
1
minimum: 2
1
1
range: - ≤ y ≤
2
2
horizontal translation: left 60°

iv

amplitude: 3
period: 180°
maximum: 3
minimum: -3
range: -3 ≤ y ≤ −3
reflection: x-axis

v

amplitude: 3
period: 720°
maximum: 2
minimum: -4
range: -4 ≤ y ≤ 2
horizontal translation: left 90°
vertical translation: down 1

vi

amplitude: 2
period: 120°
maximum: 2
minimum: -2
range: -2 ≤ y ≤ 2
horizontal translation: right 60°
reflection: x-axis

vii

amplitude: 1
period: 120°
maximum: 2
minimum: 0
range: 0 ≤ y ≤ 2
horizontal translation: right 90°
vertical translation: up 1

viii

amplitude: 2
period: 360°
maximum: 2
minimum: -2
range: -2 ≤ y ≤ 2

iii

amplitude:
I

J

9

10

y = sin ( x + 90° ) + 2

ix

amplitude: 1
period: 120°
maximum: 2
minimum: 0
range: 0 ≤ y ≤ 2
vertical translation: up 1

y = cos 3x + 1

x

amplitude: 1
period: 360°
maximum: 3
minimum: 1
range: 1 ≤ y ≤ 3
horizontal translation: left 90°
vertical translation: up 2

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Sinusoidal Sort

  • 1. y = 2 sin x A B 1 y = 3cos ( x + 90° ) − 1 2 C D E 1 y = sin ( x + 60° ) 2 F G H y = cos x + 2 y = −3sin 2x y = −2 cos 3( x − 60° ) y = cos 2x − 3 y = sin 3( x − 90° ) + 1
  • 3. i amplitude: 1 period: 360° maximum: 3 minimum: 1 range: 1 ≤ y ≤ 3 vertical translation: up 2 ii amplitude: 1 period: 180° maximum: -2 minimum: -4 range: -4 ≤ y ≤ −2 vertical translation: down 3 1 2 period: 360° 1 maximum: 2 1 minimum: 2 1 1 range: - ≤ y ≤ 2 2 horizontal translation: left 60° iv amplitude: 3 period: 180° maximum: 3 minimum: -3 range: -3 ≤ y ≤ −3 reflection: x-axis v amplitude: 3 period: 720° maximum: 2 minimum: -4 range: -4 ≤ y ≤ 2 horizontal translation: left 90° vertical translation: down 1 vi amplitude: 2 period: 120° maximum: 2 minimum: -2 range: -2 ≤ y ≤ 2 horizontal translation: right 60° reflection: x-axis vii amplitude: 1 period: 120° maximum: 2 minimum: 0 range: 0 ≤ y ≤ 2 horizontal translation: right 90° vertical translation: up 1 viii amplitude: 2 period: 360° maximum: 2 minimum: -2 range: -2 ≤ y ≤ 2 iii amplitude:
  • 4. I J 9 10 y = sin ( x + 90° ) + 2 ix amplitude: 1 period: 120° maximum: 2 minimum: 0 range: 0 ≤ y ≤ 2 vertical translation: up 1 y = cos 3x + 1 x amplitude: 1 period: 360° maximum: 3 minimum: 1 range: 1 ≤ y ≤ 3 horizontal translation: left 90° vertical translation: up 2