Chapter 4.7, Problem 50PPS

To determine

To Graph :

Graph the function.

Explanation of Solution

Given Information:

Given equation is :

  $y=h(x)=-2|x-3|+2$

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 : $f(x)=\left|x\right|=\{\begin{array}{l}x;x>0\\ -x;x\le 0\end{array}$

  $\left|x\right|\ge 0$

Domain : All real numbers

Range : All non-negative real numbers

Graph :

  

Calculation :

We have :

  $y=h(x)=-2|x-3|+2$

  $\begin{array}{l}Since\\ \left|x-3\right|\ge 0\\ \Rightarrow -2\left|x-3\right|\le 0\\ \Rightarrow -2\left|x-3\right|+2\le 0+\mathrm{2..........................}[adding"2"each\_side]\\ \Rightarrow -2\left|x-3\right|+2\le 2\end{array}$

Make a table for different value in the domain :

  $y=h(x)=-2|x-3|+2=\{\begin{array}{l}-2(x-3)+2;x-3>0\\ 2(x-3)+2;x-3\le 0\end{array}=\{\begin{array}{l}-2x+8;x>3\\ 2x-4;x\le 3\end{array}$

The center point of the absolute value graph is located where x -3 = 0. Use this x-value as the middle value in the values of the table.

x	$x-3$	$y=h(x)=-2|x-3|+2$
1	-2	-2
2	-1	0
3	0	2
4	1	0
5	2	-2

Plotting the values and joining, we get the required graph :