Features of Logarithmic Functions

• y > 3

• y > 2

• y > 1

• All Real Numbers

• x > 0

• x > 2

• x > -3

• All Real Numbers

• y > 0

• y > 2

• y > -3

• All Real Numbers

Log with a base "e" (log_e) is the same thing as...

• "e"

• Natural Logarithm (LN)

• Common Logarithm (Log)

• Natural Log, base "e"
  LN_e

• x = 2

• x = -2

• y = 2

• y = -2

• x =0

• x =-3

• y= 0 

• y= -3

• x > 3

• x > 2

• x > 1

• All Real Numbers

Describe range of the function shown: y=log₂(x+1)

• (-∞,∞)

• (-1,∞)

• (-1,3)

• (∞, -1)

f(x)=2ln(x+2)

Describe the transformation

• Vertical Stretch by 2, translation 2 units to the left

• Vertical Compression by 2, translation 2 units to the left

• Vertical Stretch by 2, translation 2 units to the right

• Vertical Compression by 2, translation 2 units to the right

Write the equation of a natural logarithmic function that has been shifted two units to the left, one unit up, and vertically stretched by a factor of three.

(Begin your answer with "y=." Use parentheses where necessary.)

Mathematical Equivalence

ON