A comedy troupe is going on tour. The amount of money in the troupe’s account C(d) is a function of the number of days d since they started the tour. The graph below shows their day-to-day account balance. Although the axes are not labeled with tick marks, you can answer the questions by using the given information and your knowledge of graphs of functions. 1. The troupe went on a 3 week tour, and the graph shows the entire 3 weeks. During that time, their greatest balance was $500.
(a) Give the domain and range of the function. Domain: 0 < D < 21
Range: 0 < C(D) < 500
(b) Give an estimate to the nearest hundreds for C(0). Explain how you determined this value and what it means in the context of this problem. C0 = 250 The Y intercept is halfway between the minimum and the maximum of the range.
(c) The troupe’s account first reached $0 on Day 11. How would you show that information in function notation? C(11) = 0
(d) The balance remained at $0 from Day 11 through Day 16. As you count segments from the left, which segment on the graph1, 2, 3, 4, 5, or 6 represents that information? Explain. Counting from the left, the 4th segment is the one that represents the information.

2. The troupe’s account balance first reached $500 on Day 4. The last day the account balance was $500 was Day 8.
(a) Determine C(5), C(6), and C(7). Explain how you determined these amounts.
(b) Estimate C(1), C(2), and C(3). Explain how you determined these amounts.
(c) The stage manager said that the amount of money taken out of the account each day between Day 8 and Day 11 was the same amount of money put into the account each day between Day 0 and Day 4. Recall that Day 11 is when the balance first reached $0. Without doing any calculations, how could you show the stage manager was incorrect?

3. On Day 17, the troupe deposited $100 into the account. On each day after Day 17, segment 5, the troupe made daily, equal deposites.
(a) Explain how you can determine, just by looking at the graph, whether the amounts deposited after Day 17 were each less than $100, $100, or more than $100.
(b) Use the graph to estimate C(21) in hundreds. Explain how you determined this estimate. How can you estimate the deposits after Day 17?