Logarithmic Functions and Their Properties

This video tutorial reviews the domain and range of logarithmic functions, focusing on log base 10 of X. It explains that the domain is all X values greater than zero, while the range is all real numbers. The video provides examples of shifted logarithmic functions, demonstrating how shifts affect the domain. It includes a practice problem for viewers to solve, reinforcing the concept of domain shifts by changing the sign of the value inside the parentheses with X.

What is the domain of log base 10 of X?

• All X values greater than one

• All real numbers

• All X values less than zero

• All X values greater than zero

What is the range of any logarithmic function?

• All X values greater than one

• All X values greater than zero

• All real numbers

• All X values less than zero

How does the graph of log base 10 of (x - 7) + 2 shift?

• Right 7 units and up 2 units

• Right 7 units and down 2 units

• Left 7 units and up 2 units

• Left 7 units and down 2 units

What is the domain of log base 10 of (x - 7) + 2?

• All X values greater than 0

• All real numbers

• All X values less than 7

• All X values greater than 7

What is a good way to remember how to find the domain of a shifted logarithmic function?

• Multiply the value inside the parentheses by X

• Divide the value inside the parentheses by X

• Switch the sign of the value inside the parentheses

• Add the value inside the parentheses to X

If a logarithmic function is shifted to the right by 2 units, what is the domain?

• All X values greater than 0

• All X values less than 2

• All X values greater than 2

• All real numbers

What happens to the graph of a logarithmic function when it is shifted to the right?

• The range changes

• The domain becomes all X values greater than the shift value

• The graph moves down

• The domain becomes all X values less than the shift value

What is the range of log base 10 of (x - 2)?

• All X values greater than 2

• All X values less than 2

• All X values greater than 0

• All real numbers

How does the graph of log base 10 of (x - 2) shift?

• Up 2 units

• Right 2 units

• Left 2 units

• Down 2 units

What is the domain of log base 10 of (x - 2)?

• All X values greater than 0

• All real numbers

• All X values less than 2

• All X values greater than 2