graph the logarithmic function.\n\n$g(x)=log_{1/2}x$\n\nplot two points on the graph of the function, and…

Explanation:

Step1: Recall log - function properties

The general form of a logarithmic function is $y = \log_{a}x$, and its vertical asymptote is $x = 0$. For $g(x)=\log_{\frac{1}{2}}x$, the vertical asymptote is $x = 0$.

Step2: Find the first point

Let $x = 1$. Then $g(1)=\log_{\frac{1}{2}}1$. Since $a^{0}=1$ for any $a>0,a\neq1$, we have $\log_{\frac{1}{2}}1 = 0$. So the point is $(1,0)$.

Step3: Find the second point

Let $x = 2$. Then $g(2)=\log_{\frac{1}{2}}2$. We know that $\left(\frac{1}{2}\right)^{- 1}=2$, so $\log_{\frac{1}{2}}2=-1$. So the point is $(2, - 1)$.

Answer:

Vertical asymptote: $x = 0$. Points: $(1,0)$ and $(2,-1)$