Find the X intercept of a logarithm with a horizontal shift

The video tutorial covers logarithmic functions, focusing on domain, range, and vertical asymptotes. It explains how to graph these functions, including shifts and transformations. The tutorial also demonstrates calculating the X-intercept and discusses potential advanced problems. The teacher emphasizes understanding the concepts to tackle more complex problems in future lessons.

What is the domain of the original logarithmic function discussed in the video?

• 3 to Infinity

• 0 to Infinity

• Negative Infinity to 0

• 1 to Infinity

How does the domain change when the function is shifted horizontally?

• It remains the same

• It changes to 3 to Infinity

• It changes to 1 to Infinity

• It changes to Negative Infinity to 3

What is the new vertical asymptote after the function is shifted?

• x = 3

• x = 0

• x = 4

• x = 1

What is the significance of the vertical asymptote in a logarithmic function?

• It shows the boundary where the function is undefined

• It is the maximum value of the function

• It is the minimum value of the function

• It indicates where the function crosses the x-axis

What happens to the graph of a logarithmic function when it is shifted to the right?

• The x-intercept moves right

• The vertical asymptote moves left

• The domain decreases

• The graph reflects over the x-axis

What is the x-intercept of the shifted logarithmic function?

• x = 1

• x = 3

• x = 0

• x = 4

How do you find the x-intercept of a logarithmic function?

• Set x to 1 and solve for y

• Set x to 0 and solve for y

• Set y to 0 and solve for x

• Set y to 1 and solve for x