Question

graph the equation by completing the table and plotting points. identify the domain.
$y = \ln x - 6$
part 1 of 3
complete the table. round to two decimal places when necessary.

x	y
0.5	-6.69
0.75	-6.29
1	-6.00
2	-5.31
3	-4.90
4	-4.61

alternate answer:

x	y
0.5	-6.69
0.75	-6.29
1	-6
2	-5.31
3	-4.9
4	-4.61

part: 1 / 3
part 2 of 3
graph the equation. plot the vertical asymptote and the points from the table.

Explanation:

Step1: Recall the domain of natural logarithm

The function is \( y = \ln x - 6 \). The natural logarithm function \( \ln x \) is defined only for \( x>0 \).

Step2: Determine the domain of the given function

Since the given function \( y=\ln x - 6 \) is a transformation (vertical shift down by 6 units) of the natural logarithm function \( \ln x \), the domain remains the same as the domain of \( \ln x \). So the domain is all real numbers \( x \) such that \( x>0 \).

Answer:

The domain of the function \( y = \ln x - 6 \) is \( (0, \infty) \) (or all positive real numbers).