Understanding Vertical Asymptotes in Logarithmic Functions

The video tutorial explains how to find the vertical asymptotes of logarithmic functions. It covers two functions: a common log function and a natural log function. For each, the video demonstrates how to rewrite the log function in exponential form, determine the domain, and find the vertical asymptote. The tutorial also includes graphical representations to illustrate how the graphs approach but never touch the vertical asymptotes, reinforcing the concept of domain restrictions.

What is the base of the logarithm in the function f(x) = log(x - 4) when no base is specified?

• Base e

• Base 10

• Base 5

• Base 2

For the function f(x) = log(x - 4), what is the domain?

• x > 4

• x > 0

• x < 4

• x < 0

What is the equation of the vertical asymptote for the function f(x) = log(x - 4)?

• x = 0

• x = 4

• x = -4

• x = 1

What is the base of the natural logarithm in the function f(x) = ln(x + 1)?

• Base e

• Base 10

• Base 2

• Base 5

For the function f(x) = ln(x + 1), what is the domain?

• x > 0

• x < 0

• x > -1

• x < -1

What is the equation of the vertical asymptote for the function f(x) = ln(x + 1)?

• x = -1

• x = 1

• x = 2

• x = 0

In the graph of f(x) = log(x - 4), what happens as x approaches 4?

• The graph touches the line x = 4

• The graph approaches but never touches the line x = 4

• The graph moves away from the line x = 4

• The graph intersects the line x = 4

In the graph of f(x) = ln(x + 1), what happens as x approaches -1?

• The graph touches the line x = -1

• The graph approaches but never touches the line x = -1

• The graph intersects the line x = -1

• The graph moves away from the line x = -1

Why does the graph of a logarithmic function never touch its vertical asymptote?

• Because the function has a minimum at the asymptote

• Because the function has a maximum at the asymptote

• Because the function is continuous at the asymptote

• Because the function is undefined at the asymptote

What is the significance of the vertical asymptote in the context of logarithmic functions?

• It represents the maximum value of the function

• It represents the minimum value of the function

• It represents a boundary that the function approaches but never reaches

• It represents a point where the function is zero