Question

A) Construct a t-chart for the function: f(x) = (1/2)^xThen Graph the function.B) domain of the function?C) range of the function?D) equation of the asymptote?E) y-intercept of the graph?

Answer 1

Answer: We need to construct a table for the given function, and then graph it and answer all the remaining parts:

`f(x)=((1)/(2))^x\Rightarrow(1)`

(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:

`D\in(\infty,\infty)\Rightarrow\text{ All real numbers}`

(C) Range of the function is:

`R\in(0,\infty)\Rightarrow\text{ All numbers greater than 0}`

(D) Equation of the asymptote.

`\begin{gathered} f(x)\Rightarrow0 \\ ((1)/(2))^x\rightarrow0\Rightarrow x=\infty \\ f(x)\Rightarrow\infty \\ ((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}`

(E) Y-intercept:

`x=0,y=1`