Logarithmic Functions and Transformations

The video tutorial explains logarithmic functions, focusing on log base 2 of x. It covers graphing the function, identifying key points, and understanding the vertical asymptote. The tutorial then demonstrates how to shift the graph and its asymptote three units to the right, affecting the domain and range. The domain changes from three to infinity, while the range remains from negative infinity to infinity.

What is the base of the logarithmic function discussed in the example?

• 2

• 3

• 10

• e

Which property of logarithms is highlighted as not being affected by the base in this example?

• The range

• The base

• The common point

• The vertical asymptote

What is the common point of the logarithmic function log base 2 of x?

• (0, 1)

• (1, 0)

• (2, 0)

• (0, 2)

What is the significance of the point (1, 0) in the graph of log base 2 of x?

• It is the x-intercept

• It is the vertex

• It is the y-intercept

• It is the asymptote

What feature of the graph is described as a vertical line that the graph approaches but never touches?

• No asymptote

• Diagonal asymptote

• Vertical asymptote

• Horizontal asymptote

How many units is the graph of log base 2 of x shifted to the right?

• 4

• 3

• 2

• 1

What transformation is applied to the graph of log base 2 of x?

• Rotation

• Translation

• Reflection

• Dilation

What does the expression x - 3 indicate in the function log base 2 of (x - 3)?

• Dilation

• Reflection

• Horizontal shift

• Vertical shift

What happens to the vertical asymptote when the graph is shifted?

• It disappears

• It stays the same

• It moves right

• It moves left

What is the new position of the vertical asymptote after the graph is shifted?

• x = 3

• x = 2

• x = 1

• x = 0