Chapter 1.9, Problem 21E

To determine

To graph: The equation $y=1+\left|x-1\right|$ is an appropriate viewing rectangle.

Explanation of Solution

Given information:

The equation $y=1+\left|x-1\right|$ .

Graph:

For the graph of equation $y=1+\left|x-1\right|$ firstly set the suitable values of $\text{a,b,c,d}$ for viewing rectangles.

Take values $\left[\text{0,1}\right]\times \left[\text{0,}\frac{1}{2}\right]$ then resulting graph is blank because $\left|x-1\right|\ge 0$ so $1+\left|x-1\right|\ge 1$ for all the $x$ .

  

Thus, graph lies above the viewing rectangle, so this viewing rectangle is not appropriate.

The graph of the equation $y=1+\left|x-1\right|$ can be sketched using the traces,

For thevalue $x=0$ , the trace of the equation is,

  $\begin{array}{c}y=1+\left|0-1\right|\\ =1+1\\ =2\end{array}$

For the value $x=1$ , the trace of the equation is,

  $\begin{array}{c}y=1+\left|1-1\right|\\ =1\end{array}$

For the plane $x=2$ , the trace of the equation is,

  $\begin{array}{c}y=1+\left|2-1\right|\\ =1+1\\ =2\end{array}$

For the different values of $x$ get different values of $\text{y}$ .

The whole graph is lies above of the $x$ axes. So, the values of $y$ should be greater or equal to 1.

Take values $\left[\text{-10,10}\right]\times \left[\text{-10,10}\right]$

  

The resulting graph is appropriate viewing rectangle.

For enlarge the viewing rectangle change the values of $\text{a,b,c,d}$ .

Interpretation:

The graph of an equation in a viewing screen is a viewing rectangle.

The $\text{x}$ -values to range from a minimum value of $\text{xmin}$ $=\text{a}$ to a maximum value of $\text{xmax}$ $=\text{b}$

The $\text{y}$ -values to range from minimum value of $\text{ymin}$ $=\text{c}$ to a maximum value of $\text{ymax}$ $=\text{d}$

Then, the display portion of the graph lies in the rectangle $\left[\text{a,b}\right]\times \left[\text{c,d}\right]=\left\{\left(\text{x,y}\right)|\text{a}\le \text{x}\le \text{b},\text{c}\le \text{y}\le \text{d}\right\}$

The graph of $y=1+\left|x-1\right|$ is appropriate in $\left[\text{-10,10}\right]\times \left[\text{-10,10}\right]$ viewing rectangle