1. **State the problem:** We are given two functions: $f(x) = \log x$ and $g(x) = \log(x - 1) + 1$. We need to graph both on the same viewing rectangle and describe the relationship between their graphs. 2. **Recall the properties of logarithmic functions:** The graph of $f(x) = \log x$ has a vertical asymptote at $x=0$ and increases slowly to the right. 3. **Analyze the transformation for $g(x)$:** The function $g(x) = \log(x - 1) + 1$ is a horizontal shift of $f(x)$ by 1 unit to the right (due to $x-1$ inside the log) and a vertical shift of 1 unit upward (due to the $+1$ outside the log). 4. **Vertical asymptote of $g(x)$:** Since $f(x)$ has a vertical asymptote at $x=0$, shifting right by 1 moves the asymptote to $x=1$. 5. **Graph comparison:** On the same axes, $g(x)$ will look like $f(x)$ but shifted right by 1 and up by 1. This means the curve of $g$ starts near $x=1$ and is always 1 unit above the corresponding point on $f$. 6. **Conclusion:** The correct graph is option A, which shows $g(x)$ shifted right by 1 and up by 1 relative to $f(x)$, with the vertical asymptote at $x=1$ for $g$ and at $x=0$ for $f$. **Final answer:** The graph of $g(x)$ is the graph of $f(x)$ shifted 1 unit to the right and 1 unit up.