Transforming Logarithmic Functions

Write the transformed function: f(x)=ln x is stretched by a factor of 3, reflected across the x-axis, and shifted by 2 units to the left.

• g(x) = -3 ln (x+2)

• g(x) = -1/3 ln (x-2)

• g(x) = 3 ln (x-2)

• g(x) = -ln (3x+2)

Where is the asymptote?

• x = 1

• y = 1

• x = -1

• y = -1

What are the transformations of this graph?

• Right 1 Up 5

• Right 1 Down 5

• Left 1 Up 5

• Left 1 Down 5

• Reflection across the y-axis, shrink by a factor of 3, horizontal shift left 7 

• Reflection across the asymptote, horizontal shift right 3, vertical shift down 7 

• Reflection across the asymptote, stretch by a factor of 3, vertical shift down 7 

• Stretch by a factor of 3, vertical shift down 7 

Use y=log(x) as a parent function. To graph y=log(x-4)+7, the parent function should be translated vertically ​ (a)   (up or down) by ​ ​ (b)   units. The vertical asymptote should be shifted horizontally to the ​ (c)   (left or right) by ​ (d)   units.

• up

• right

• 4

• down

• left

• 7

Select all the transformations that apply.

y = 3log ₃ (2x)

• Vertical stretch by 3

• Vertical shrink by 1/3

• Horizontal shrink by 1/2

• Horizontal stretch by 2

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

Describe the transformations of f(x)= -log₂(x+1)

• left 1

• left one & reflected over the y-axis

• left one & reflected over the x-axis

• right one & reflected over the x axis

Describe the transformation on

• The graph has been shifted 3 units up

• The graph has been shifted 3 units to the right

• The graph has been shifted 2 units right

• The graph has been shifted 3 units left

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