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 with base 10 and a natural log function with base e. The tutorial demonstrates how to rewrite these functions in exponential form to determine their domains and vertical asymptotes. It also includes graphical representations to verify the findings, emphasizing that the graph approaches but never touches the vertical asymptote line.

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

• Base e

• Base 5

• Base 10

• Base 2

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

• x > 0

• x > 4

• 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 = 1

• x = -4

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

• Base 2

• Base e

• Base 10

• Base 5

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

• x < -1

• x < 0

• x > -1

• x > 0

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

• x = 1

• x = 0

• x = 2

• x = -1

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

• The graph intersects the line x = 4

• The graph touches the line x = 4

• The graph moves away from the line x = 4

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

• The graph intersects the line x = -1

Why can't the graph of f(x) = log(x - 4) touch the line x = 4?

• Because log(x - 4) becomes undefined

• Because log(x - 4) becomes positive

• Because log(x - 4) becomes negative

• Because log(x - 4) becomes zero

What is the significance of a vertical asymptote in a logarithmic function?

• It indicates where the function is maximum

• It indicates where the function is undefined

• It indicates where the function is zero

• It indicates where the function is minimum