Chapter 4.7, Problem 44PPS

(a)

To determine

To Draw:

A table of values where x is all integers from -5 to 5 , inclusive.

Explanation of Solution

Given Information:

  $f(x)=\left|2x+3\right|$

Concept Used :

Absolute Value Function:

An absolute value function is a function that contains an algebraic expression within absolute value symbols. The absolute value of a number is its distance from 0 on the number line. Parent Function : $f(x)=\left|x\right|=\{\begin{array}{l}x;x>0\\ -x;x\le 0\end{array}$

Domain : All real numbers

Range : All non-negative real numbers

Graph :

   $f(x)=\left|x\right|$

Calculation:

Make a table :

x	2x+3	$f(x)=\left|2x+3\right|$
-5	-7	7
-4	-5	5
-3	-3	3
-2	-1	1
-1	1	1
0	3	3
1	5	5
2	7	7
3	9	9
4	11	11
5	13	13

(b)

To determine

To Plot :

The points of the table on a coordinate grid.

Explanation of Solution

Given Information:

From part (a)

x	$f(x)=\left|2x+3\right|$
-5	7
-4	5
-3	3
-2	1
-1	1
0	3
1	5
2	7
3	9
4	11
5	13

Graph:

Plot the points in the table on the graph:

  

(c)

To determine

To Graph :

The function.

Explanation of Solution

Given Information:

From part (b)

  

Graph:

Join the points with straight line :

  

We get the graph :