Learn how to graph the natural log function with a horizontal shift

The video tutorial explains the appearance and characteristics of logarithmic graphs, focusing on how different bases affect the graph's shape. It covers transformations, specifically horizontal shifts, and how these shifts affect the graph's asymptote. The tutorial concludes with expectations for homework, emphasizing the importance of showing shifted asymptotes.

What is the common point through which all logarithmic graphs pass, regardless of their base?

• (1, 0)

• (0, 1)

• (1, 1)

• (0, 0)

How does the base of a logarithmic function affect its graph?

• It alters the graph's vertical asymptote.

• It changes the graph's starting point.

• It affects the speed of the graph's curve.

• It changes the graph's horizontal asymptote.

What happens to a logarithmic graph when you add a constant to the variable?

• The graph becomes flatter.

• The graph shifts vertically.

• The graph shifts horizontally.

• The graph becomes steeper.

When a logarithmic graph is shifted horizontally, what happens to its asymptote?

• It remains unchanged.

• It shifts vertically.

• It disappears.

• It shifts horizontally.

After shifting a logarithmic graph 3 units to the left, what is the new position of the point (1, 0)?

• (-2, 0)

• (4, 0)

• (-3, 0)

• (1, 3)