(-2, 4)

(-∞, ∞)

(-∞, 0)

(∞, -∞)

y = log₆(-x) + 1

y = log₆(x − 2) + 1

y = log₆(x + 2) - 1

y = log(x-8) + 1

"e"

Natural Logarithm (LN)

Common Logarithm (Log)

Natural Log, base "e"
LN_e

x = 2

x = -2

y = 2

y = -2

y = log₅ (x + 1) + 1 

y = log₅ (x - 1) + 1 

y = log₅ (x²) + 1 

y = log₅ (x)-1

y = 0

x = 0

(-∞, ∞)

(0, ∞)

[1, ∞)

(1, ∞)

Horizontal shift left 1

Horizontal shift right 1

Vertical shift up 5

Vertical shift down 5

x = -3

x=5

y= -3

y=5

(2, 0)

(-1, 0)

(0, 1)

(1, 0)

x = 1

y = 1

x = -1

y = -1

Exponential Growth

Exponential Decay

Logarithmic

D: all real numbers
R: y > 0

Domain: all real numbers
Range: all real numbers

Domain: x > 0
Range: all real numbers

Domain: all real numbers
Range: y < 0

$$x>1$$

$$x<1$$

$$y>1$$

$$y<1$$

translate right 21 units and 50 units down

translate left 21 units and 50 units down

translate right 21 units and 50 units up

translate left 21 units and 50 units up

All real numbers

$$x>1$$

$$y<2$$

$$y>1$$