Chapter 3.3, Problem 13Q

To determine

To graph the linear function:

  $p\left(x\right)=-3x-1$

Answer to Problem 13Q

Explanation of Solution

Given:

  $p\left(x\right)=-3x-1$

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 graph the linear function:

  $p\left(x\right)=-3x-1$

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,

  $\begin{array}{c}p\left(-2\right)=-3\left(-2\right)-1\\ =6-1\\ =5,\\ p\left(-1\right)=-3\left(-1\right)-1\\ =3-1\\ =2\end{array}$

  $\begin{array}{c}p\left(0\right)=-3\left(0\right)-1\\ =0-1\\ =-1,\\ p\left(1\right)=-3\left(1\right)-1\\ =-3-1\\ =-4,\text{ and }\\ p\left(2\right)=-3\left(2\right)-1\\ =-6-1\\ =-7\end{array}$

Thus, input output table of given linear function is:

$x$	$-2$	$-1$	0	1	2
$p\left(x\right)$	5	2	$-1$	$-4$	$-7$

This input-output table gives the ordered pairs that satisfies graph of the given function: $\left(-2,5\right),\left(-1,2\right),\left(0,-1\right),\left(1,-4\right),\left(2,-7\right)$ .

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: