Understanding Graphs and Logarithmic Functions

This video tutorial covers graphing logarithmic and natural logarithmic functions, focusing on transformations, domain, and range. It explains how to set up equations for graphing, apply transformations, and plot points for accurate sketches. The tutorial also discusses the effects of reflections and shifts on graphs, providing a comprehensive guide to understanding and graphing these functions.

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

• All real numbers

• x > 0

• x = 0

• x < 0

How does the graph of y = -log(x) differ from y = log(x)?

• It shifts to the left

• It reflects over the y-axis

• It reflects over the x-axis

• It shifts to the right

If a logarithmic function is transformed by y = log(x + 3), what happens to the graph?

• It reflects over the x-axis

• It shifts 3 units to the left

• It reflects over the y-axis

• It shifts 3 units to the right

What is the range of any logarithmic function?

• x = 0

• All real numbers

• x > 0

• x < 0

In the function y = log base 3 (x + 2) - 1, what is the vertical asymptote?

• x = -2

• x = 2

• x = 0

• x = 1

What is the base of a natural logarithm?

• 10

• 2

• 1

• e

How does the graph of y = ln(x) compare to y = log(x)?

• ln(x) is a reflection of log(x)

• log(x) is steeper

• ln(x) is steeper

• They are identical

What happens to the graph of y = ln(x) when transformed to y = ln(x + 1)?

• It shifts 1 unit to the right

• It reflects over the x-axis

• It shifts 1 unit to the left

• It reflects over the y-axis

In the function y = 2 - ln(3 - x), what is the vertical asymptote?

• x = 3

• x = -3

• x = 2

• x = 0

What is the domain of the function y = 2 - ln(3 - x)?

• x < 3

• All real numbers

• x > 3

• x = 3