Chapter 4.7, Problem 45PPS

(a)

To determine

To Draw:

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

Explanation of Solution

Given Information:

  $f(x)=\left|2x\right|+3$

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	$f(x)=\left|2x\right|+3$
-5	-10	13
-4	-8	11
-3	-6	9
-2	-4	7
-1	-2	5
0	0	3
1	2	5
2	4	7
3	6	9
4	8	11
5	10	13

(b)

To determine

To Plot :

The points of the table on a coordinate grid.

Explanation of Solution

Given Information:

From part (a)

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

  

(d)

To determine

To Explain:

How this graph is different from the graph shown below :

  

Explanation of Solution

Given Information :

From part (c) and given , the two graph are :

  

  

Observation:

Merging the two graph :

  

The graph $f(x)=\left|2x\right|+3$ is shifted 1.5 units to the right and 3 units up from the graph $f(x)=|2x+3|$ .

When the constant is outside the absolute value symbol, the graph is shifted vertically. If the constant is inside the absolute value symbol, the graph is shifted horizontally.