1. **State the problem:** We need to graph the logarithmic function $$g(x) = \log_{\frac{1}{5}} x$$ and identify which graph (A, B, C, or D) correctly represents it. 2. **Recall the properties of logarithms:** - The base here is $$\frac{1}{5}$$, which is between 0 and 1. - For logarithms with base $$a$$ where $$0 < a < 1$$, the function is decreasing. - The domain is $$x > 0$$. - The graph passes through the point $$(1,0)$$ because $$\log_a 1 = 0$$ for any valid base $$a$$. 3. **Behavior of $$g(x) = \log_{\frac{1}{5}} x$$:** - As $$x \to 0^+$$, $$g(x) \to +\infty$$ because the log function with base less than 1 goes to positive infinity near zero. - As $$x \to +\infty$$, $$g(x) \to -\infty$$. 4. **Analyze the given graphs:** - Graphs A and B show the graph starting near $$y=10$$ at $$x\to 0^+$$ and decreasing as $$x$$ increases, which matches the behavior of $$g(x)$$. - Graphs C and D show the graph increasing as $$x$$ increases, which is incorrect for base $$\frac{1}{5}$$. 5. **Distinguish between A and B:** - Both A and B describe similar behavior, but B explicitly states the graph is mostly in the top-left quadrant and approaches the x-axis from above as $$x$$ increases. - This matches the expected behavior of $$g(x)$$. **Final answer:** The correct graph is **B**. $$\boxed{\text{Graph B}}$$