Understanding Logarithmic Functions and Graphs

The video tutorial explores the investigation of values between zero and one using powers of two. It explains the deliberate choice of numbers for analysis and demonstrates the construction of a graph with selected points. The tutorial guides viewers through plotting points and drawing a curve, ultimately analyzing the graph's properties, including its asymptote and intercepts.

Why is it important to choose values purposefully between zero and one?

• To make the graph look symmetrical

• To save time during calculations

• To ensure a more accurate investigation

• To avoid using negative numbers

What is the significance of choosing numbers like 1, 2, 4, and 8?

• They are all even numbers

• They are all prime numbers

• They are powers of two

• They are multiples of three

Which of the following is a power of two between zero and one?

• 1/6

• 1/3

• 1/4

• 1/5

What is the y-value when x is 1/8 on the graph?

• 0

• -2

• -1

• -3

How would you describe the point (1, 0) on the graph?

• It is above the x-axis

• It is at the origin

• It is on the x-axis

• It is on the y-axis

What shape does the graph take when plotted?

• A straight line

• A circle

• A curve

• A parabola

What is the equation of the graph discussed in the lesson?

• y = x/2

• y = x^2

• y = log base 2 of x

• y = 2^x

What is the x-intercept of the graph?

• (0, 1)

• (0, 0)

• (2, 0)

• (1, 0)

Why is there no y-intercept on this graph?

• The graph is a parabola

• The graph is a circle

• The graph is a straight line

• The graph never crosses the y-axis

What is the term for a line that a graph approaches but never touches?

• Chord

• Asymptote

• Intercept

• Tangent