5.06 Logarithmic Transformations

Horizontal

100

log₂(x-4)

moves to the right 4 (h=4)

200

h=-3 

moves to the left

log₂(x+3)

300

log₂(x+1)

moves to the left 1 (h=-1)

400

h=1

moves to the right 1

log₂(x-1)

500

log₂(x+5)

moves to the left 5 (h=-5)

Vertical

100

log₂x + 3

moves up 3, k = 3

200

k= -2 

moves down 2

log₂x - 2

300

log₂x - 4

moves down 4, k= -4

400

k= 2

moves up 2 

log₂x + 2

500

log₂x - 5 

moves down 5, k= -5

Advanced

100

log₂(x-3)+2

moves right 3 and up 2

200

moves right 1 and down 2

log₂(x-1) - 2

300

Reflects over the y-axis

x values change

log₂(-x)

400

reflects over the x axis

y values change

-log₂(x)

500

-log₂(x+2)-2

flips over the x axis

moves left 2 and down 2