Chapter 1.8, Problem 28E

a.

To determine

To find: the type of function.

Answer to Problem 28E

Piecewise function

Explanation of Solution

Given information:

Labor charges are $55 per hour or any fraction of an hour.

Calculation:

Let number of hours be x. and labor cost be L. The table for the given situation will be as follows:

Number of hours( $x$)	Labor cost ($)( $L$)
$0<x\le 1$	55
$1<x\le 2$	110
$2<x\le 3$	165
$3<x\le 4$	220
$4<x\le 5$	275

Since the table shows different non-linear rates, the function of labor charge due to number of hours should be a piecewise function.

b.

To determine

To find: the function for the given situation.

Answer to Problem 28E

  $L\left(x\right)=\{\begin{array}{l}55\text{ if }0<x\le 1\\ 110\text{ if 1}<x\le 2\\ 165\text{ if 2}<x\le 3\\ 220\text{ if 3}<x\le 4\\ 275\text{ if 4}<x\le 5\end{array}$

Explanation of Solution

Given information:

Given situation is a labor charge as a function of time.

Labor charges are $55 per hour or any fraction of an hour.

Number of hours( $x$)	Labor cost ($)( $L$)
$0<x\le 1$	55
$1<x\le 2$	110
$2<x\le 3$	165
$3<x\le 4$	220
$4<x\le 5$	275

Calculation:

From the table, the expression for labor charge as a function of time is as follows:

  $L\left(x\right)=\{\begin{array}{l}55\text{ if }0<x\le 1\\ 110\text{ if 1}<x\le 2\\ 165\text{ if 2}<x\le 3\\ 220\text{ if 3}<x\le 4\\ 275\text{ if 4}<x\le 5\end{array}$

c.

To determine

To graph: the function.

Answer to Problem 28E

  

Explanation of Solution

Given information:

Labor charges are $55 per hour or any fraction of an hour.

Number of hours( $x$)	Labor cost ($)( $L$)
$0<x\le 1$	55
$1<x\le 2$	110
$2<x\le 3$	165
$3<x\le 4$	220
$4<x\le 5$	275

Calculation: