Understanding Logarithmic Functions

This video tutorial explains how to graph a logarithmic function by hand. It covers determining the domain, range, and vertical asymptote of the function. The video also demonstrates how to isolate the logarithm, convert it to an exponential equation, and use it to complete a table of values. Finally, it shows how to plot points and sketch the graph, ensuring it approaches the vertical asymptote.

What is the primary goal of the video tutorial?

• To understand the Pythagorean theorem

• To learn about trigonometric identities

• To graph a logarithmic function and determine its properties

• To solve a quadratic equation

For the function log base 3 of (x + 1), what is the domain?

• x > 0

• x > -1

• x < 0

• x < -1

What is the equation of the vertical asymptote for the function log base 3 of (x + 1)?

• x = 0

• x = 1

• x = -1

• x = 2

What is the range of the basic logarithmic function?

• x > 0

• x = 0

• All real numbers

• x < 0

How does multiplying by 2 and subtracting 3 affect the range of the function?

• It makes the range finite

• It does not change the range

• It shifts the range upwards

• It shifts the range downwards

What is the first step in graphing the logarithmic function by hand?

• Drawing the asymptote

• Finding the domain

• Isolating the logarithm

• Plotting points

What is the equivalent exponential equation for log base 3 of (x + 1)?

• 3^(y+3)/2 = x + 1

• 3^(y-3)/2 = x - 1

• 3^(y+1)/3 = x + 3

• 3^(y-1)/3 = x - 3

When y = -3, what is the corresponding x value?

• x = 0

• x = 2

• x = 1

• x = -1

What is the ordered pair when y = 1?

• (8, 1)

• (0, 1)

• (2, 1)

• (1, 8)

What does the graph of the function approach?

• The vertical asymptote

• The y-axis

• The origin

• The x-axis