Question

this could be the graph of:
a. $\ln(x + 3)-4$
b. $\ln(x)+4$
c. $\ln(x + 3)$
d. $\ln(x - 3)+4$

Explanation:

Step1: Analyze the vertical shift

The graph of \(y = \ln(x)\) has a vertical asymptote at \(x = 0\) and passes through \((1,0)\). The given graph seems to have a vertical shift upwards. For a function \(y=\ln(x - h)+k\), the vertical shift is determined by \(k\).

Step2: Analyze the horizontal shift

The vertical asymptote of the given graph is at \(x = 3\). For the function \(y=\ln(x - h)\), the vertical asymptote is at \(x=h\). So \(h = 3\) (horizontal shift of 3 units to the right).

Answer:

D. \(\ln(x - 3)+4\)