Chapter SH, Problem 8.12EP

To determine

To graph: the function by making the table.

Answer to Problem 8.12EP

The function is valid for $\text{x}\ne \text{3}$ .

Explanation of Solution

Given:

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

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:

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

Table:

$\text{x}$	$\text{-2}$	$\text{-1}$	$\text{0}$	$\text{1}$	$\text{2}$
$\text{y}$	$\text{0}\text{.8}$	$\text{0}\text{.5}$	$\text{0}$	$\text{-1}$	$\text{-4}$

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

  

Here by putting $\text{x=3}$ the function will be not defined so, $\text{x}$ should not be equal to $\text{3}$ .

Hence, the function is valid for $\text{x}\ne \text{3}$ .