Transforming Graphs of Logarithms

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

• x=1

• x=-1

• y=1

• y=-1

• left 3, right 1

• right 3, down 1

• right 3, up 1

• left 3, down 1

Which graph matches the function

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

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How has the graph transformed?

Red is parent graph

Blue is transformation

• left 1 up 6

• left 2 up 4

• left 2 up 6

• up 6

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

What are the transformations of this graph?

• Right 1 Up 5

• Right 1 Down 5

• Left 1 Up 5

• Left 1 Down 5

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

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Determine the order of transformations

• left 1, reflected over x-axis

• up 1, reflected over y-axis

• right 1, reflected over x-axis

• left 1, reflected over y-axis