Transformations of Exponential and Logarithmic Functions

Logarithmic functions are the inverse of...

• Linear Functions

• Exponential Functions 

• Quadratic Functions 

• Polynomial Functions 

Classify the following graph.

• Exponential Growth

• Exponential Decay

• Logarithmic

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

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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

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

What are the transformations of this graph?

• Right 1 Up 5

• Right 1 Down 5

• Left 1 Up 5

• Left 1 Down 5

Write the equation of a natural logarithmic function that has been shifted two units to the left, one unit up, and vertically stretched by a factor of three. (Begin your answer with "y=." Use parentheses where necessary.)

Mathematical Equivalence

ON

Write the equation of a natural logarithmic function that has been shifted two units to the left, one unit up, and vertically stretched by a factor of three.

(Begin your answer with "y=." Use parentheses where necessary.)

Mathematical Equivalence

ON

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