Logarithmic and Exponential Functions

This video tutorial explains how to graph a logarithmic function by hand. It covers the domain, range, and vertical asymptote of the function y = log base 1/2 of x. The video demonstrates converting the logarithmic function to its equivalent exponential form and using a table of values to plot points. It also explains how to sketch the graph, highlighting key points and the vertical asymptote. The tutorial concludes with a summary of the graphing process.

What is the domain of the logarithmic function y = log base 1/2 of x?

• (-∞, ∞)

• [0, ∞)

• (-∞, 0)

• (0, ∞)

What is the range of the logarithmic function y = log base 1/2 of x?

• [0, ∞)

• (0, ∞)

• (-∞, 0)

• (-∞, ∞)

What is the equation of the vertical asymptote for the function y = log base 1/2 of x?

• y = 1

• x = 1

• x = 0

• y = 0

What is the equivalent exponential form of y = log base 1/2 of x?

• x = 2^y

• x = y^2

• x = 2^(-y)

• x = 1/2^y

When y = 0, what is the value of x in the exponential form of the function?

• 0

• 1

• 1/2

• 2

When y = 1, what is the value of x in the exponential form of the function?

• 2

• 1/2

• 1

• 1/4

What is the value of x when y = 2 in the exponential form of the function?

• 1/4

• 1/2

• 1

• 2

How can the base 1/2 be rewritten using powers of 2?

• 2^(-1)

• 2^2

• 2^0

• 2^1

What is the x-coordinate when y = -2 using the rewritten exponential form?

• 1/2

• 1/4

• 2

• 4

Which point is the horizontal intercept of the graph?

• (0, 1)

• (1, 0)

• (1/2, 1)

• (4, -2)