Logarithmic Graphs

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Which function has a vertical asymptote?

• exponential

• logarithm

• both

• neither

What is the  Vertical Asymptote?

• x=5

• x=0

• y=0

• x=1

What's the corresponding graph of

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f(x)=log₅(x+4) - 2

Describe the asymptote

• Horizontal Asymptote x = -4

• Vertical Asymptote x = -4

• Horizontal Asymptote x = 4

• Vertical Asymptote x = 4

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

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