evaluate y = ln (x - 2) for the following values of x. round to the nearest thousandth. x = 3, y = 0 √ x =…

Explanation:

Step1: Recall properties of logarithmic functions

The function $y = \ln(x - 2)$ is a natural - logarithm function. The domain of $y=\ln(u)$ is $u>0$. For $y = \ln(x - 2)$, we have $x-2>0$, so the domain is $x > 2$. The vertical asymptote of the function $y=\ln(x - 2)$ is $x = 2$.

Step2: Analyze key points

When $x=3$, $y=\ln(3 - 2)=\ln(1)=0$; when $x = 4$, $y=\ln(4 - 2)=\ln(2)\approx0.693$; when $x = 6$, $y=\ln(6 - 2)=\ln(4)\approx1.386$. The graph of $y = \ln(x)$ is shifted 2 units to the right to get $y=\ln(x - 2)$.

Step3: Identify the correct graph

The graph that has a vertical asymptote at $x = 2$ and passes through the points $(3,0)$, $(4,0.693)$ and $(6,1.386)$ (approximately) is the correct one. The first graph has a vertical asymptote at $x = 2$ and the correct general shape for a natural - logarithm function shifted 2 units to the right.

Answer:

The first graph (the one on the left - hand side)