Chapter R, Problem 1RE

These review exercises are for test preparation. They can also serve as a practice test. Answers are at the back of the book Red bracketed section references indicate the part(s) of the chapter to restudy if your answer is incorrect

Concept Reinforcement

For each equation in column A, select the most appropriate graph in column B. [R.1, R.4, R.5]

Column A	Column B
$y=\left|x\right|$

To determine

The correct match for the graph of the function $y=\left|x\right|$ from column B.

Answer to Problem 1RE

Solution:

The correct match for the graph of the function $y=\left|x\right|$ from column B is (d).

Explanation of Solution

Given information:

The graphs provided in Column B:

Consider the function,

$y=\left|x\right|$

The modulus function is defined as

$\begin{array}{ccc}\hfill f\left(x\right)& =& \left|x\right|\hfill \\ \hfill & =& \{\begin{array}{c}\hfill x,x\ge 0\\ \hfill -x,x<0\end{array}\hfill \end{array}$

Now, the table for ordered pair $\left(x,y\right)$ for the function $f\left(x\right)=\left|x\right|$ is shown below:

x	$f\left(x\right)$
0	0
1	1
2	2
-1	1
-2	2

So, the resulting graph is,

Hence, the correct match is part (d).