Chapter 1.3, Problem 64E

To determine

To calculate: To graph the sketch of piecewise-defined function

Explanation of Solution

  

Given: Function is $f\left(x\right)=\left\{\begin{array}{l}1-{\left(x-1\right)}^2,x\le 2\\ \sqrt{x-2},x>2\end{array}\right\}$

Calculation:

Function is given as follows:

  $f\left(x\right)=\left\{\begin{array}{l}1-{\left(x-1\right)}^2,x\le 2\\ \sqrt{x-2},x>2\end{array}\right\}$

Calculate the value of function at different values of $x$

When $x\le 2$

x	-2	-1	0	1	2
$f\left(x\right)=1-{\left(x-1\right)}^2$	-8	-3	0	1	0

When $x>2$

x	3	6	11	18	27
$f\left(x\right)=\sqrt{x-2}$	1	2	3	4	5

On plotting the above points on graph:

  

Conclusion:

Hence, graph of function is sketched