5 Trig Transformations

Question 1

Vertical Translation Up

Answer 1

y = f(x) + a, a>0

Question 2

Vertical Translation Down

Answer 2

y = f(x) - a, a>0

a>0

Question 3

Horizontal Translation Left

Answer 3

y = f(x+a), a>0

Question 4

Horizontal Translation Right

Answer 4

y = f(x-a), a>0

Question 5

Vertical Stretch

Answer 5

y = a·f(x), a>1

Question 6

Vertical Compression

Answer 6

y = (1/a)·f(x), a>1

Question 7

Horizontal Compression

Answer 7

y = f(a·x), a>1

Question 8

Horizontal Stretch

Answer 8

y = f(1/a · x), a>1

Question 9

Horizontal Reflection

Answer 9

y = f(-x) OR
y = f(-1·x)

Question 10

Vertical Reflection

Answer 10

y = - f(x) OR
y = -1·f(x)

Question 11

Compress Sine vertically by 3

Answer 11

y = (1/3)·sin x

Question 12

Stretch Sine vertically by 4

Answer 12

y = 4·sin x

Question 13

Shift sine left by 45°

Answer 13

y = sin(x + 45°)

Question 14

Shift sine right by 180°

Answer 14

y = sin(x - 180°)

Question 15

Shift sine up by 3

Answer 15

y = sin x + 3

Question 16

Shift sine down by 1

Answer 16

y = sin x - 1

Question 17

Compress sin horizontally by 5

Answer 17

y = sin (5x)

Question 18

Stretch sine horizontally by 2

Answer 18

y = sin (1/2 · x)

Question 19

Compress sine horizontally by 2 and shift up by 4

Answer 19

y = sin(2x) + 4

Question 20

Shift sine down by 3 and left by 90°

Answer 20

y = sin(x + 90°) - 3

Question 21

Shift sine right by 45° and up by 2

Answer 21

y = sin(x - 45°) + 2

Question 22

Stretch sine vertically by 10, shift right by 5° and down by 2

Answer 22

y = 10 sin(x - 5°) - 2