1. The problem is to analyze the function $y=\log_{\frac{1}{2}} x$. 2. The logarithm function $y=\log_a x$ is defined for $x>0$ and base $a>0$, $a \neq 1$. 3. Here, the base is $\frac{1}{2}$, which is between 0 and 1, so the logarithm is a decreasing function. 4. The function passes through the point $(1,0)$ because $\log_a 1=0$ for any valid base $a$. 5. The domain is $x>0$ and the range is all real numbers. 6. The function has a vertical asymptote at $x=0$. 7. The graph decreases from $+\infty$ as $x$ approaches 0 from the right, to $-\infty$ as $x$ grows large. Final answer: The function $y=\log_{\frac{1}{2}} x$ is a decreasing logarithmic function with domain $x>0$, range $(-\infty, \infty)$, vertical asymptote at $x=0$, and passes through $(1,0)$.