Understanding Logarithmic Functions

The video tutorial explores the graph of a logarithmic function, specifically y = log base 2 of x. It begins by introducing the graph and potential function definitions, encouraging viewers to think about which function is depicted. The tutorial then explains the basic form of the logarithmic function, providing examples and graphing points to illustrate its behavior. It discusses the graph's behavior as x approaches zero and infinity, highlighting the asymptotic nature and domain restrictions. Finally, the video examines transformations, such as flipping and shifting the graph, to understand how these affect the function's appearance.

What should you do before continuing with the video?

• Pause the video and think about the function definitions.

• Skip to the end of the video.

• Write down all the function definitions.

• Ignore the graph and focus on the text.

What is the base of the logarithm in the function definitions?

• Base 10

• Base e

• Base 2

• Base 5

What is the value of log base 2 of 8?

• 2

• 3

• 1

• 4

What happens to the value of y when x is 1/2 in the function y = log base 2 of x?

• y becomes -1

• y becomes 1

• y becomes 2

• y becomes 0

What is the general shape of the graph of y = log base 2 of x?

• A straight line

• A parabola

• An exponential curve

• A logarithmic curve

What happens to the value of y as x approaches 0 from the right in the function y = log base 2 of x?

• y becomes undefined

• y becomes very positive

• y becomes zero

• y becomes very negative

What is the domain of the function y = log base 2 of x?

• Non-positive x values

• Negative x values

• Positive x values

• All real numbers

How does the graph of y = -log base 2 of x differ from y = log base 2 of x?

• It is flipped over the x-axis.

• It is shifted down.

• It is flipped over the y-axis.

• It is shifted up.

What transformation is applied to the graph of y = -log base 2 of x to get the blue graph?

• Shifted down by 2

• Shifted to the left by 2

• Shifted up by 2

• Shifted to the right by 2

What is the new asymptote of the function y = -log base 2 (x + 2)?

• x = 0

• x = -2

• x = -1

• x = 2