Chapter 4, Problem 24CR

To determine

To find: The function and the graph for the function that represents the relationship between the number of $x$ days and the total cost $y$ in dollars of renting the popcorn machine.

Answer to Problem 24CR

The required function is $f\left(x\right)=\{\begin{array}{l}65,0<x\le 1\\ 100,0<x\le 2\\ 135,0<x\le 3\end{array}$ and the graph for the function is shown in Figure 1

Explanation of Solution

Given:

The fair is of 3 days.

The first day charge is $65 and then $35 for the additional day.

Calculation:

Consider the table for the given information is shown in Table 1

Table 1

Number of days	Total cost (dollars)
$0<x\le 1$	65
$0<x\le 2$	100
$0<x\le 3$	135

Then, the step function for the above table is,

  $f\left(x\right)=\{\begin{array}{l}65,0<x\le 1\\ 100,0<x\le 2\\ 135,0<x\le 3\end{array}$

The required plot for the above function is shown in Figure 1

  

Figure 1