Answer: We need to construct a table for the given function, and then graph it and answer all the remaining parts:
[tex]f(x)=(\frac{1}{2})^x\Rightarrow(1)[/tex]
(a) The table for function (1) Is as follows:
The plot is as follows:
(B) Domain of the function:
The domin of the function can be determined by inspecting the graph, therefore the domain is as follows:
[tex]D\in(\infty,\infty)\Rightarrow\text{ All real numbers}[/tex]
(C) Range of the function is:
[tex]R\in(0,\infty)\Rightarrow\text{ All numbers greater than 0}[/tex]
(D) Equation of the asymptote.
[tex]\begin{gathered} f(x)\Rightarrow0 \\ (\frac{1}{2})^x\rightarrow0\Rightarrow x=\infty \\ f(x)\Rightarrow\infty \\ (\frac{1}{2})^x=\frac{1}{2^x^{}}\rightarrow\infty \\ \therefore\rightarrow \\ 2^x=0\rightarrow(1) \\ \text{ The equation (1) is only true for the largest negative number} \end{gathered}[/tex]
(E) Y-intercept:
[tex]x=0,y=1[/tex]
