Transformation of Log Graphs

Write the equation of the function f(x)=log₃x after the following transformations:

Translate 6 units left and 4 units up.

• g(x)=log₃(x+6)+4

• g(x)=log₃(x+4)-6

• g(x)=log₃(x-6)+4

• g(x)=3log(x+6)+4

Write the equation of the function f(x)=log(x+5)-6 after the following transformations:
Translate 3 units left and 2 units up.

• f(x)=log(x+2)+2

• f(x)=log(x+2)-4

• f(x)=log(x+8)-4

• f(x)=log(x+8)+2

Write the equation of the function f(x)=3logx+4 after the following transformations:
Vertical stretch by a factor of 2, translate 5 units to the right.

• g(x)=5log(x+5)+4

• g(x)=5log(x-5)+4

• g(x)=6log(x-1)

• g(x)=6log(x-5)+4

find the asymptote: y = log₁₀ (x+3)

• x=-3

• x=3

• y=-3

• y=3

What are the transformations of this graph?

• Right 1 Up 5

• Right 1 Down 5

• Left 1 Up 5

• Left 1 Down 5

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

Which graph matches the function

*remember the transformation has shifted it right 3 and down 3

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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

• 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 

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

• left one & y-axis reflection

• right one & y-axis reflection

• left one & x-axis reflection

• right one & x-axis reflection