Chapter 11.3, Problem 8E

To determine

To find: Calculate the domain of the function and sketch the graph of the function.

Answer to Problem 8E

The domain of the function is $-\infty <x<\infty$ .

Explanation of Solution

Given information: The function is $f\left(x\right)=9{\left(\frac{2}{3}\right)}^x$

To draw a graph of the given function, need to prepare a table of value of in depended variable of x and dependent variable y .

Let, $x=0,1,\text{ and 2}$

  $\begin{array}{cccc}x& 0& 1& 2\\ y& 9& 6& 4\end{array}$

Hence, the graph is

  

From the graph, it is clear that the function is defined for all value of x .

Hence, $\text{Domain}\text{of}9{\left(\frac{2}{3}\right)}^x:\left[\begin{array}{cc}\text{Solution}:& -\infty <x<\infty \\ \text{Interval}\text{Notation}:& \left(-\infty ,\infty \right)\end{array}\right]$