Understanding if a logarithmic function is continuous or not

What is the basic form of the natural logarithm function?

• y = ln(x)

• y = e^x

• y = x^2

• y = log(x)

Which of the following best describes the domain of the natural logarithm function?

• Positive integers only

• Zero to infinity

• Negative numbers only

• All real numbers

What does the presence of a vertical asymptote in the graph of a logarithmic function indicate?

• The function has a hole

• The function is not continuous

• The function is defined for all real numbers

• The function is continuous within its domain

How does shifting a logarithmic graph horizontally and vertically affect its continuity?

• It does not affect the continuity

• It changes the domain of the function

• It removes the vertical asymptote

• It makes the graph discontinuous

What happens to the graph of y = ln(x) when it is shifted 3 units to the right and 2 units up?

• The graph becomes discontinuous

• The graph remains continuous

• The graph's domain changes

• The vertical asymptote disappears