1. The problem is to analyze the function $f(x) = \log x$ and understand its domain, range, and behavior. 2. The logarithmic function $f(x) = \log x$ is defined only for positive values of $x$, so its domain is $\{x \mid 0 < x < \infty\}$. 3. The range of $f(x) = \log x$ is all real numbers, $\{y \mid -\infty < y < \infty\}$, because as $x$ approaches 0 from the right, $\log x$ approaches $-\infty$, and as $x$ increases without bound, $\log x$ increases without bound. 4. The function is increasing, not decreasing, as $x$ approaches 0 from the right; it actually decreases towards $-\infty$ but the function itself is increasing overall. 5. To summarize: - Domain: $0 < x < \infty$ - Range: $-\infty < y < \infty$ - Behavior: $f(x)$ increases as $x$ increases. This matches the statement: "The graph is not explicitly shown but is implied to be the function of $f(x) = \log x$, where $x$ is in the domain $(0, \infty)$ and the range is $(-\infty, \infty)$". Hence, the correct domain and range for $f(x) = \log x$ are: $$\text{Domain: } (0, \infty)$$ $$\text{Range: } (-\infty, \infty)$$