Chapter 1.2, Problem 32E

To determine

To graph: The piecewise function $f\left(x\right)=\{\begin{array}{l}1,x<0\\ \sqrt{x},x\ge 0\end{array}$.

Explanation of Solution

Given information: The piecewise function is $f\left(x\right)=\{\begin{array}{l}1,x<0\\ \sqrt{x},x\ge 0\end{array}$.

Graph:

To graph a function $f\left(x\right)=\{\begin{array}{l}1,x<0\\ \sqrt{x},x\ge 0\end{array}$ , follow the steps using graphing calculator.

First press “ON” button on graphical calculator, press $\boxed{\text{Y}=}$ key and enter right hand side of the equation $f\left(x\right)=\{\begin{array}{l}1,x<0\\ \sqrt{x},x\ge 0\end{array}$ after the symbol ${\text{Y}}_1$ . Enter the keystrokes $\boxed{1}\boxed{/}\boxed{(}\boxed{\text{X}}\boxed{2\text{nd}}\boxed{\text{MATH}}\boxed{5}\boxed{0}\boxed{)}$ . Now press Enter after the symbol ${\text{Y}}_2$ . Enter the keystrokes $\boxed{\text{X}}\boxed{^}\boxed{(}\boxed{1}\boxed{÷}\boxed{2}\boxed{)}\boxed{/}\boxed{(}\boxed{\text{X}}\boxed{2\text{nd}}\boxed{\text{MATH}}\boxed{4}\boxed{0}\boxed{)}$.

The display will show the equations,

  $\begin{array}{l}{\text{Y}}_{\text{1}}=\left(1\right)/\left(\text{X}<0\right)\\ {\text{Y}}_2=\text{X}^\left(1/2\right)/\left(\text{X}\ge 0\right)\end{array}$

Now, press the $\boxed{\text{GRAPH}}$ key and $\boxed{\text{TRACE}}$ key to produce the graph of given function in standard window as shown below.

  

Figure (1)

Interpretation:

The graph of the piecewise function $f\left(x\right)=\{\begin{array}{l}1,x<0\\ \sqrt{x},x\ge 0\end{array}$ is a straight line parallel to $x$ -axis with equation $y=1$ for $x<0$ and a curve $\sqrt{x}$ for $0\le x$.