Understanding Logarithmic Functions and Transformations

The video tutorial explains how to determine the domain, range, and vertical asymptote of the function g(x) = -log base 3 of x + 4. It begins with a review of logarithmic functions and their properties, including domain and range. The tutorial then analyzes the function g(x), discussing its domain, range, and vertical asymptote. Graphical transformations are used to verify these properties, showing how g(x) is a transformation of the basic log function. The video concludes with a verification of the domain, range, and asymptotes, emphasizing that the range remains all real numbers despite transformations.

What is the base of the logarithmic function given in the problem?

• 2

• 3

• 5

• 4

For the basic logarithmic function y = log base 3 of x, what is the domain?

• x ≤ 0

• x ≥ 0

• x < 0

• x > 0

What is the range of the basic logarithmic function y = log base 3 of x?

• x ≥ 0

• x < 0

• x > 0

• All real numbers

What is the horizontal intercept of the basic log function y = log base 3 of x?

• (0, 0)

• (1, 1)

• (1, 0)

• (0, 1)

What transformation is applied to reflect the graph of the basic log function across the x-axis?

• Rotation

• Reflection

• Horizontal shift

• Vertical shift

How does adding 4 to the function g(x) = -log base 3 of x affect its graph?

• Reflects it across the x-axis

• Shifts it down 4 units

• Shifts it up 4 units

• Reflects it across the y-axis

What is the vertical asymptote of the function g(x) = -log base 3 of x + 4?

• y = 1

• y = 0

• x = 1

• x = 0

As x approaches zero from the right, what happens to the function values of g(x)?

• Approach zero

• Remain constant

• Approach negative infinity

• Approach infinity

Does the graph of g(x) have a horizontal asymptote?

• Yes, at y = 4

• Yes, at y = -4

• Yes, at y = 0

• No, it does not have a horizontal asymptote

What is the range of the function g(x) = -log base 3 of x + 4?

• x > 0

• All real numbers

• x < 0

• x ≥ 0