Understanding Logarithmic Functions

The video tutorial explains how to graph a logarithmic function by hand, focusing on the function y = -log base 3 of x. It covers identifying the domain, range, and vertical asymptote, and demonstrates how to convert the logarithmic equation into an exponential form to calculate points for graphing. The tutorial provides step-by-step instructions for plotting these points and sketching the graph, emphasizing the importance of accuracy and understanding the function's behavior.

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

• The open interval from negative infinity to zero

• The open interval from negative infinity to positive infinity

• The open interval from zero to infinity

• The closed interval from zero to infinity

How does the negative sign in y = -log base 3 of x affect the domain, range, and vertical asymptote?

• It does not change the domain, range, or vertical asymptote

• It changes the domain

• It changes the range

• It changes the vertical asymptote

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

• Calculating the range

• Drawing the vertical asymptote

• Isolating the logarithm

• Plotting points on the graph

When converting the logarithmic equation to an exponential equation, what is the resulting form?

• b raised to the power of x equals y

• b raised to the power of negative y equals x

• b raised to the power of negative x equals y

• b raised to the power of y equals x

Why do we select y-values instead of x-values when calculating points for the graph?

• Because x is in the position of the exponent

• Because it changes the domain

• Because it simplifies the calculation

• Because y is in the position of the exponent

If y = 0, what is the corresponding x-value in the exponential equation 3^(-y) = x?

• 9

• 3

• 1

• 0

What is the x-value when y = -1 in the equation 3^(-y) = x?

• 9

• 3

• 1/3

• 1

What is the approximate x-value when y = -1.5 in the equation 3^(-y) = x?

• 5.2

• 4.5

• 2.5

• 6.3

What is the purpose of sketching the vertical asymptote before plotting points?

• To guide the graphing process

• To calculate the x-values

• To identify the domain

• To determine the range

What does the graph of the function approach as it extends to the left?

• The vertical asymptote

• The origin

• The y-axis

• The x-axis