Chapter 1.2, Problem 33E

To determine

To graph:The piecewise function $f\left(x\right)=\{\begin{array}{l}4-x^2,x<1\\ \left(3/2\right)x+3/2,1\le x\le 3\\ x+3,x>3\end{array}$ .

Explanation of Solution

Given information:The piecewise function is $f\left(x\right)=\{\begin{array}{l}4-x^2,x<1\\ \left(3/2\right)x+3/2,1\le x\le 3\\ x+3,x>3\end{array}$ .

Graph:

To graph a function $f\left(x\right)=\{\begin{array}{l}4-x^2,x<1\\ \left(3/2\right)x+3/2,1\le x\le 3\\ x+3,x>3\end{array}$ , 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 piecewise functions. Enter the keystrokes $\boxed{\text{(}}\boxed{4}\boxed{-}\boxed{\text{X}}\boxed{x^2}\boxed{)}\boxed{÷}\boxed{(}\boxed{\text{X}}\boxed{2\text{nd}}\boxed{\text{MATH}}\boxed{5}\boxed{1}\boxed{)}$ . Press enter after the symbol ${\text{Y}}_2$ . Enter the keystrokes $\boxed{(}\boxed{\text{3X}}\boxed{÷}\boxed{2}\boxed{)}\boxed{+}\boxed{\text{3}}\boxed{÷}\boxed{2}\boxed{÷}\boxed{(}\boxed{1}\boxed{2\text{nd}}\boxed{\text{MATH}}\boxed{5}\boxed{\text{X}}\boxed{)}\boxed{(}\boxed{\text{X}}\boxed{2\text{nd}}\boxed{\text{MATH}}\boxed{5}\boxed{3}\boxed{)}$ .Now, press Enter after the symbol ${\text{Y}}_3$ andenter the keystrokes $\boxed{\text{X}}\boxed{+}\boxed{3}\boxed{/}\boxed{(}\boxed{\text{X}}\boxed{2\text{nd}}\boxed{\text{MATH}}\boxed{3}\boxed{3}\boxed{)}$ .

The display will show the equations,

  $\begin{array}{l}{\text{Y}}_{\text{1}}=4-{\text{X}}^2/\left(\text{X}<1\right)\\ {\text{Y}}_2=\left(\text{3X}/2\right)+3/2/\left(1\le \text{X}\right)\left(\text{X}\le 3\right)\\ {\text{Y}}_3=\text{X}+3/\left(\text{X}>3\right)\end{array}$

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

  

Figure (1)

Interpretation:

The graph of the piecewise function $f\left(x\right)=\{\begin{array}{l}4-x^2,x<1\\ \left(3/2\right)x+3/2,1\le x\le 3\\ x+3,x>3\end{array}$ is a parabola defined for $x<1$ and straight lines for $1\le x\le 3$ and $x>3$ .