1. **Problem Statement:** Identify which function corresponds to the given graph. 2. **Given options:** - $f(x) = \ln x$ - $f(x) = \log(2x)$ - $f(x) = -e^{2x}$ - $f(x) = 2e^x$ 3. **Key characteristics of each function:** - $\ln x$ is a logarithmic function defined for $x>0$, starting near $y=-\infty$ as $x\to0^+$ and increasing slowly. - $\log(2x)$ is also logarithmic, similar shape to $\ln x$ but shifted/scaled. - $-e^{2x}$ is an exponential decay function, rapidly decreasing. - $2e^x$ is an exponential growth function, rapidly increasing. 4. **Analyzing the graph description:** - The curve starts just above 0 at $x=0$ and rises slowly. - The shape is consistent with a logarithmic curve. - The graph is defined for positive $x$ values. 5. **Conclusion:** The graph matches the behavior of $f(x) = \ln x$. **Final answer:** $$f(x) = \ln x$$