Exponential and Logarithmic Transformations and Characteristics

Exponential Functions and Logarithmic Functions are

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

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

What ordered pair is on every logarithmic parent function? ​ (a)  

• (1, 0)

• (0, 1)

• (0,0)

• cannot be determined without the function

A student is analysing the following characteristics of a logarithmic function: 1) x-intercept, 2) equation of the vertical asymptote, 3) the domain, 4) the range. When the graph of the logarithmic function is stretched vertically by a factor of 2, reflected horizontally about the y-axis and translated 3 units up, how many of the four characteristics listed above will stay the SAME?