Logarithmic Functions and Their Properties

The video tutorial explains how to graph the function y = log base 2 of x by hand. It begins by converting the logarithmic equation into its exponential form, 2^y = x, to simplify the process of creating a table of values. By selecting y values and calculating corresponding x values, the tutorial demonstrates plotting points on a graph. It highlights the behavior of the graph, including the vertical asymptote at x = 0. The video concludes with a discussion on the properties of logarithmic functions, such as domain, range, and intercepts.

What is the equivalent exponential form of the logarithmic equation y = log base 2 of x?

• 2^y = x

• y^2 = x

• x^2 = y

• 2^x = y

When completing a table of values for y = log base 2 of x, why is it easier to select y values first?

• Because y values are always positive

• Because it simplifies finding corresponding x values

• Because x values are always negative

• Because y values are always integers

What is the x value when y = -1 in the equation 2^y = x?

• 2

• 1/2

• 1

• 4

Which point is NOT plotted on the graph of y = log base 2 of x?

• (1, 0)

• (1/2, -1)

• (3, 2)

• (8, 3)

What happens to the graph of y = log base 2 of x as it approaches the y-axis?

• It crosses the y-axis

• It touches the y-axis

• It gets closer but never touches the y-axis

• It moves away from the y-axis

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

• y = 1

• x = 1

• y = 0

• x = 0

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

• (-∞, 0)

• (0, ∞)

• (-∞, ∞)

• (1, ∞)

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

• (1, ∞)

• (-∞, 0)

• (-∞, ∞)

• (0, ∞)

If the base of a logarithmic function is greater than 1, what is the behavior of the function?

• Decreasing

• Constant

• Oscillating

• Increasing

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

• (0, 1)

• (2, 0)

• (0, 0)

• (1, 0)