Understanding Logarithmic Functions

This video tutorial explains how to graph a logarithmic function by hand. It covers finding the domain, range, and vertical asymptote of the function. The tutorial also demonstrates converting the logarithmic equation to an exponential form to plot points and sketch the graph accurately.

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

• x ≥ 0

• x < 0

• x ≤ 0

• x > 0

For the function log base 2 of (x-3), what is the domain?

• x ≤ 3

• x > 3

• x < 3

• x ≥ 3

What is the equation of the vertical asymptote for the function log base 2 of (x-3)?

• x = -3

• x = 0

• x = 3

• x = 2

What is the range of a basic logarithmic function?

• x > 0

• All real numbers

• x ≥ 0

• x < 0

How does adding a constant to the output of a log function affect its range?

• The range becomes positive numbers only

• The range remains all real numbers

• The range becomes negative numbers only

• The range becomes non-negative numbers

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

• Determine the range

• Isolate the logarithm

• Find the domain

• Sketch the vertical asymptote

How do you convert a logarithmic equation to an exponential form?

• By raising the base to the power of the log's output

• By multiplying the base by the log's output

• By subtracting the base from the log's output

• By adding the base to the log's output

When graphing, why do we select y-values instead of x-values for the table?

• Because y is in the exponent position

• Because x is in the exponent position

• Because y is easier to calculate

• Because x is easier to calculate

What is the x-value when y equals 2 in the function log base 2 of (x-3)?

• 4

• 5

• 6

• 7

What is the approximate x-value for the horizontal intercept when y equals 0?

• 6.25

• 4.25

• 5.25

• 3.25