Explanation
We must plot the function:
[tex]f(x)=\log_{\frac{1}{2}}(x).[/tex]
With values -10 ≤ x ≤ 10 and -10 ≤ y ≤ 10.
Taking into account the properties of logarithms:
[tex]\begin{gathered} \log_a(x^b)=b\cdot\log_a(x), \\ \log_a(a)=1. \end{gathered}[/tex]
We evaluate the function at x = 1/2, 1, 2, 4 and 8:
[tex]\begin{gathered} f(\frac{1}{2})=\log_{\frac{1}{2}}(\frac{1}{2})=1, \\ f(1)=\log_{\frac{1}{2}}(1)=0, \\ f(2)=\operatorname{\log}_{\frac{1}{2}}(2)=\operatorname{\log}_{\frac{1}{2}}((\frac{1}{2})^{-1})=-1\cdot\operatorname{\log}_{\frac{1}{2}}(\frac{1}{2})=-1, \\ f(4)=\operatorname{\log}_{\frac{1}{2}}(4)=\operatorname{\log}_{\frac{1}{2}}((\frac{1}{2})^{-2})=-2\cdot\operatorname{\log}_{\frac{1}{2}}(\frac{1}{2})=-2, \\ f(8)=\operatorname{\log}_{\frac{1}{2}}(8)=\operatorname{\log}_{\frac{1}{2}}((\frac{1}{2})^{-3})=-3\cdot\operatorname{\log}_{\frac{1}{2}}(\frac{1}{2})=-3. \end{gathered}[/tex]
Plotting these values and the function, we get the following graph:
Answer
Points:
• (1/2, 1)
,
• (1, 0)
,
• (2, -1)
,
• (4, -2)
,
• (8, -3)
Graph:
