Chapter SH, Problem 8.13EP

To determine

To graph: the function by making the table.

Answer to Problem 8.13EP

The function is valid for $\text{x}\ne -2$ .

Explanation of Solution

Given:

  $\text{f}\left(\text{x}\right)\text{=}\frac{\text{x-4}}{\text{x+2}}$ .

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:

  $\text{f}\left(\text{x}\right)\text{=}\frac{\text{x-4}}{\text{x+2}}$ .

Table:

$\text{x}$	$\text{-1}$	$\text{0}$	$\text{1}$	$\text{2}$
$\text{y}$	$\text{-5}$	$-2$	$\text{-1}$	$\text{-0}\text{.5}$

The graph of given function $\text{f}\left(\text{x}\right)\text{=}\frac{\text{x-4}}{\text{x+2}}$ is:

  

Here by putting $\text{x=-2}$ the function will be not defined so, $\text{x}$ should not be equal to $-2$ and function has zeroes at $\text{x=4}$ .

Hence, the function is valid for $\text{x}\ne -2$ .