Graph a logarithmic function with multiple transformations

The video tutorial explains the relationship between logarithmic and exponential functions, highlighting their inverse nature. It covers the graphing of logarithmic functions, focusing on transformations such as shifts and the movement of asymptotes. The tutorial also discusses the domain and range of these functions, emphasizing the importance of understanding graph limits and asymptotes.

What is the relationship between logarithmic and exponential functions?

• They are both linear functions.

• They have no relationship.

• They are inverse functions of each other.

• They are the same type of function.

What is the x-intercept of a logarithmic function?

• (1, 1)

• (0, 0)

• (1, 0)

• (0, 1)

How does a negative horizontal shift affect the graph of a logarithmic function?

• It moves the graph down.

• It moves the graph to the left.

• It moves the graph to the right.

• It moves the graph up.

What happens to the vertical asymptote when a logarithmic graph is shifted to the right?

• It becomes horizontal.

• It moves to the left.

• It remains unchanged.

• It moves to the right.

What is the domain of a logarithmic function after a rightward shift?

• x > 0

• All real numbers

• x < 4

• x > 4