Characteristics and Transformations of Exponential and Logarithmic Functions

Logarithmic Functions are ​ (a)   ​ (b)  

• one-to-one functions

• monotonic functions

• always increasing

• have one extrema

Mathematical Equivalence

ON

The range of logarithmic functions ​ (a)  

• is all real numbers

• is from the vertical asymptote to infinity

• cannot be determined without having the function

Mathematical Equivalence

ON

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

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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(s) of the function when compared to its parent function.

• Translation up 2 units and translation right 1 unit

• Translation down 2 units and Translation left 1 unit

• Translation left 2 units and Translation up 1 unit

• Translation right 2 units and Translation down 1 unit