Question

Find the domain, x -intercept, and vertical asymptote of the logarithmic function and sketch its graph.

Answer 1

Step 1:

The function is

Use the natural logarithmic function : .

The function is defined only if , therefore the domain of the function is .

The domain of the function is .

Step 2:

To find the -intercept ,

Substitute in function

The -intercept  is at .

Step 3:

The function has vertical asymptote at .

Vertical asymptote is

Graph:

Solution :

The domain of the function is .

The -intercept  is at .

Vertical asymptote is