Chapter SH, Problem 7.2EP

To determine

To graph: the function and state the domain and range.

Answer to Problem 7.2EP

The domain here is all real number $\{\text{x}\in \text{R}\}$ and range here is greater than $0$ can be represent as: $\{y\ge -3\}$ .

Explanation of Solution

Given:

  $\text{f}\left(\text{x}\right){\text{=2}}^{\text{3}}{}^{\text{x}}-3$ .

Concept used:

The graph of the function $\text{f}$ is the set of all point in the plane of the form $\left(\text{x,f}\left(\text{x}\right)\right)$ .

The graph can be defined by the graph of $\text{f}$ and the equation for the graph will be $\text{y=f}\left(\text{x}\right)$ .

The tabular data of domain as $\text{x}$ and range $\text{y}$ while connecting the point to form curve which can be plot as graph using graphing calculator.

Calculation:

  $\text{f}\left(\text{x}\right){\text{=2}}^{\text{3}}{}^{\text{x}}-3$ .

Table:

$\text{x}$	$\text{-2}$	$\text{-1}$	$\text{0}$	$\text{1}$	$\text{2}$
$\text{y}$	$-2.98$	$-2.875$	$-2$	$5$	$61$

The domain here is all real number and range here is greater than $-3$ .

The graph of given function $\text{f}\left(\text{x}\right){\text{=2}}^{\text{3}}{}^{\text{x}}-3$ is:

  

Hence, the domain here is all real number $\{\text{x}\in \text{R}\}$ and range here is greater than $0$ can be represent as: $\{y\ge -3\}$ .