Logarithmic Transformations

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

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

• (-∞,∞)

• (-1,∞)

• (-1,3)

• (∞, -1)

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

• (-∞,∞)

• (-1,∞)

• (-1,3)

• (∞, -1)

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

Select all of the transformations of f(x)=lnx that produce the function

g(x)= − log x+3

• vertical stretch by e

• Reflection over the y-axis

• Translation 3 units left

• Reflection over the x-axis

• Translation 3 units up

Select all of the transformations of f(x)=log₅x that produce the function g(x)=8log₅(x-4)

• Vertical stretch by a factor of 8

• Vertical stretch by 5

• Translation 4 units left

• Translation 4 units right

• Translation 4 units down

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

Write the equation of the function f(x)=log(x+5)-6 after the following transformations:

Translate 3 units left and 2 units up.

• g(x)=log(x+2)+2

• g(x)=log(x+2)-4

• g(x)=log(x+8)-4

• g(x)=log(x+8)+2

Logarithms and Exponentials are what?

• parallel
• perpendiular 
• inverses
• congurent