Graphing the Natural Logarithm Function

The video tutorial explains how to graph the function f(x) = ln(2x) by first determining the domain, selecting x values, calculating corresponding y values using a calculator, and then plotting the graph by hand. The tutorial emphasizes understanding the behavior of the graph as x approaches zero, highlighting the logarithmic nature of the function.

What is the function f(x) that we are graphing?

• f(x) = xln(2)

• f(x) = ln(x)

• f(x) = 2ln(x)

• f(x) = ln(2x)

Why must the input to the logarithm function be greater than zero?

• Logarithms of negative numbers are undefined

• Logarithms can be any real number

• Logarithms can only be zero

• Logarithms must be positive

What is the domain of the function f(x) = ln(2x)?

• x ≥ 0

• x < 0

• All real numbers

• x > 0

What is the correct expression for the domain of the function f(x) = ln(2x)?

• 2x ≥ 0

• x ≥ 0

• 2x > 0

• x > 0

Which x value is NOT used in the video for plotting?

• 3

• 0.1

• 1.5

• 2.5

What is the y value when x = 1 in the function f(x) = ln(2x)?

• 0.69

• 2

• 1

• 0

What is the y value when x = 0.5 in the function f(x) = ln(2x)?

• 0

• 0.5

• -1

• 1

At which x value does the function f(x) = ln(2x) reach a y value of approximately 1.79?

• 3

• 2.5

• 2

• 1.5

What happens to the graph of f(x) = ln(2x) as x approaches zero?

• It approaches zero

• It remains constant

• It becomes infinitely positive

• It becomes infinitely negative

What is the behavior of the function f(x) = ln(2x) as x becomes very large?

• Approaches zero

• Becomes infinitely negative

• Remains constant

• Becomes infinitely large