Understanding the Natural Logarithm Function

The video tutorial explores the function y = ln(x - 3), focusing on its domain, plotting, and behavior near x = 3. The domain is defined for x > 3, as the natural log requires positive inputs. The function is plotted, showing it intersects the x-axis at x = 4. As x approaches 3 from the right, the function's value decreases towards negative infinity, indicating a vertical asymptote at x = 3.

What is the function y defined as in the video?

• y = ln(x)

• y = ln(3 - x)

• y = ln(x - 3)

• y = ln(x + 3)

For which values of x is the function y = ln(x - 3) defined?

• x > 3

• x = 3

• x < 3

• x ≤ 3

What is the x-intercept of the function y = ln(x - 3)?

• (3, 0)

• (4, 0)

• (0, 4)

• (0, 3)

What happens to the function y = ln(x - 3) as x approaches 3 from the right?

• It approaches positive infinity

• It approaches zero

• It approaches negative infinity

• It remains constant

What is the vertical asymptote of the function y = ln(x - 3)?

• x = 3

• x = 0

• x = -3

• x = 4

What is the value of y when x = 3.1 for the function y = ln(x - 3)?

• -4.6

• -6.9

• 0

• -2.3

What is the value of y when x = 3.01 for the function y = ln(x - 3)?

• 0

• -6.9

• -4.6

• -2.3

What is the value of y when x = 3.001 for the function y = ln(x - 3)?

• -2.3

• 0

• -4.6

• -6.9

What is the behavior of the function y = ln(x - 3) as x approaches 3 from the right?

• The function becomes zero

• The function remains constant

• The function becomes negative

• The function becomes positive

What is the domain of the function y = ln(x - 3)?

• x < 3

• x ≤ 3

• x > 3

• x = 3