Chapter 1.3, Problem 72E

To determine

To calculate: To graph the function and to determine whether the function is even, odd or neither

Answer to Problem 72E

Function is an neither an even function nor an odd function

Explanation of Solution

  

Given: Function is $f\left(x\right)=-\left|x-5\right|$

Formula Used:

Even Function: If the graph of function has symmetry about y-axis as shown below:

  

Odd Function: If the graph of function has symmetry about origin as shown below:

  

Calculation:

Function is given as follows:

  $f\left(x\right)=-\left|x-5\right|$

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

x	1	3	5	7	9
$f\left(x\right)=-\left|x-5\right|$	-4	-2	0	-2	-4

On plotting the above points on graph:

  

Since the graph of function is neither symmetric about y-axis nor about the origin, thus the function is neither an even function nor an odd function

Conclusion:

Hence, graph of function is sketched and function is neither an even function nor an odd function