Chapter 3.3, Problem 23E

To determine

To graph the linear function:

$p\left(x\right)=4x$

Answer to Problem 23E

Explanation of Solution

Given:

$p\left(x\right)=4x$

Concept Used:

To graph a linear function $f\left(x\right)=ax+b$ :

1. Make an input-output table to find ordered pairs.
2. Plot the ordered pairs.
3. Draw a line through the points in above step.

Calculation:

In order to graph the linear function:

$p\left(x\right)=4x$

First, make an input-output table, by finding value of $p\left(x\right)$ at some values of x, say at $x=-2,-1,0,\text{ 1, and 2}$ . As,

$\begin{array}{c}p\left(-2\right)=4\left(-2\right)\\ =-8,\\ p\left(-1\right)=4\left(-1\right)\\ =-4,\end{array}$

$\begin{array}{c}p\left(0\right)=4\left(0\right)\\ =0,\\ p\left(1\right)=4\left(1\right)\\ =4,\text{ and }\\ p\left(2\right)=4\left(2\right)\\ =8\end{array}$

Thus, input output table of given linear function is:

x	$-2$	$-1$	0	1	2
$p\left(x\right)$	$-8$	$-4$	0	4	8

From this input output table we get the ordered pairs: $\left(-2,-8\right),\left(-1,-4\right),\left(0,0\right),\left(1,4\right),\left(2,8\right)$ .

Now finally to draw the graph of given linear function plot these ordered pair using a graphing utility and draw a line through them. The graph is represented as: