y = 2sin x y = 3cos 12x + 90°( ) −1

y = cos x + 2 y = −2cos3 x − 60°( )

y = 12sin x + 60°( ) y = cos2x − 3

y = −3sin2x y = sin 3 x − 90°( ) +1

A B

C D

E F

G H

1 2

3 4

5 6

7 8

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

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

amplitude: 12

period: 360°

maximum: 12

minimum: - 12

range: - 12≤ y ≤

12

horizontal translation: left 60°

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

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

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

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

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

i ii

iii iv

v vi

vii viii

y = sin x + 90°( ) + 2 y = cos3x +1

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

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

I J

9 10

ix x