Transforming Graphs of Logarithms

What is the equation of the asymptote?

• x = -3

• x=5

• y= -3

• y=5

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

Which graph matches the equation

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Which equation matches the graph

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Logarithmic functions are the inverse of _________________

• exponential functions

• linear functions

• quadratic functions

• cubic functions

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

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)=2ln(x+2)

Describe the asymptote

• Horizontal asymptote x = -2

• Horizontal asymptote x = 2

• Vertical asymptote x = -2

• Vertical asymptote x = 2

f(x)=2ln(x+2)

Find the Domain and Range

• Domain: (-∞, ∞)

  Range: ( -2, ∞)

• Domain: (-∞, ∞)

  Range: ( -∞, -2)

• Domain: ( -∞, -2)

  Range: (-∞, ∞)

• Domain: ( -2, ∞)

  Range: (-∞, ∞)

f(x)=¼ ln(x - 2) + 3

Describe the asymptote

• Horizontal asymptote x=2

• Horizontal asymptote x= -2

• Vertical asymptote x=2

• Vertical asymptote x= -2