Logarithmic Transformations

Logarithmic functions are the inverse of...

• Linear Functions
• Exponential Functions 
• Quadratic Functions 
• Polynomial Functions 

Select all the transformations that apply.

y = -2 log _1/2 x

• Vertical stretch by 2

• Vertical shrink by 1/2

• Reflection across the y-axis

• Reflection across the x-axis

Match the graph with its equation

• y = log₅ (x + 1) + 1 
• y = log₅ (x - 1) + 1 
• y = log₅ (x²) + 1 
• y = log₅ (x)-1

What is the Range?

• y > 0
• All Real Numbers
• y > 1
• y < 1

What is the equation of the asymptote?

• x = -3
• x=5
• y= -3
• y=5

Describe the graph of f(x) = log x changed to

f(x) = 3log(x + 1) - 5

• vertical stretch by 3 and shift right 1 and 5 units down

• vertical stretch by 3 and shift left 1 and 5 units down

• vertical compress by 3 and shift right 1 and 5 units down

• vertical compress by 3 and shift left 1 and 5 units down

Select all the transformations that apply.

y = log ₅ (x + 1) +1

• Horizontal shift left 1

• Horizontal shift right 1

• Vertical shift up 1

• Vertical shift down 1

Find the domain and range of:
f(x) = log₂(x)

• D: all real numbers
  R: y > 0
• Domain: all real numbers
  Range: all real numbers
• Domain: x > 0
  Range: all real numbers
• Domain: all real numbers
  Range: y < 0

The asymptote of y = log₂(x + 2) will shift...

• right two to x = 2

• left two to x = -2

• not shift and remain x = 0

The asymptote of y = log₂x + 1 will shift...

• right one to x = 1

• left one to x = -1

• not shift at all and remain x = 0