Graphing logarithmic equations

The video tutorial explains how to graph a logarithmic function with a vertical shift. It begins by introducing the concept of transformations and how they affect the graph. The instructor then demonstrates graphing the logarithm without transformations, followed by applying transformations to the graph. Key points include plotting specific points, understanding the asymptote, and shifting the graph vertically. The tutorial concludes with a finalized graph, maintaining the domain and range properties.

What happens to the graph of a function when a constant is added outside the logarithmic function?

• The graph becomes steeper.

• The graph shifts vertically.

• The graph shifts horizontally.

• The graph becomes flatter.

How can you simplify the process of plotting points for a logarithmic function?

• By using a calculator to find random points.

• By rewriting the logarithmic equation in exponential form.

• By guessing the points based on the graph's shape.

• By using only the x-intercept.

What are the chosen x-values for plotting the parent graph of the logarithmic function?

• X = 2 and X = 4

• X = 3 and X = 5

• X = 0 and X = 2

• X = 1 and X = 3

After applying a vertical shift, what remains unchanged in the graph of a logarithmic function?

• The slope of the graph

• The domain and range

• The position of the asymptote

• Both the domain and the asymptote

What is the new y-coordinate of the point (3, 1) after a vertical shift of 4 units up?

• 7

• 5

• 3

• 1