Graph Logarithm

f(x)=log₅(x+4) - 2

Find the Domain and Range

• Domain: x ≥ -4

  Range: all real numbers

• Domain: all real numbers

  Range: y ≥ -4

• Domain: all real numbers

  Range: y > -4

• Domain: x > -4

  Range: all real numbers

f(x)=log₅(x+4) - 2

Describe the transformation

• translation 4 units to the right, 2 units down

• translation 4 units to the left, 2 units down

• translation 4 units to the up, 2 units right

• translation 4 units to the up, 2 units left

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

f(x)=¼ ln(x - 2) + 3

Find the Domain and Range

• Domain: all real numbers

  Range: y > 2

• Domain: all real numbers

  Range: y > -2

• Domain: x > -2

  Range: all real numbers

• Domain: x > 2

  Range: all real numbers

f(x)=¼ ln(x - 2) + 3 Describe the transformation

• Vertical Stretch by 1/4, translation 2 units right, 3 units up

• Vertical Compression by 1/4, translation 2 units right, 3 units up

• Vertical Stretch by 1/4, translation 2 units left, 3 units up

• Vertical Compression by 1/4, translation 2 units left, 3 units up

• Base is 3; x-intercept:  (1, 0)

• Base is 3; x-intercept is (0, 1)

• Base is 1; x intercept: (0, 3)

• Base is 1; x-intercept is (3, 0) 

What transformation takes place based on the equation? y = log(x+3)

• left 3

• right 3

• up 3

• down 3

• vertical stretch by a factor of 3

What are the translations of this graph?

• Right 1 Up 5

• Right 1 Down 5

• Left 1 Up 5

• Left 1 Down 5

What is the range of the logarithmic function y = log(x)?

• All real numbers

• Only negative numbers

• Only positive numbers

• All Integers

• y > 0

What is the vertical shift of the logarithmic function y = log(x) + 3?

• 3

• 4

• 2

• 1

• 0