The amount in Ebony’s bank account is a function of the number of days d since she opened the account. The graph shows segments representing her day-by-day bank balance. Although there are no labeled tick marks on the graph, you can answer the questions by using the additional given information as well as your general knowledge of graphs of functions.
(graph)
1. Ebony kept her bank account open for only 3 weeks, and the graph shows the entire 3 weeks. During that time, her greatest balance was $400.
(a) Give the domain and range of the function.
(b) Give an estimate to the nearest hundreds for . Explain how you determined your estimate and tell what means in context of the situation.
(c) Ebony’s bank balance first reached $0 on Day 12. How would you show that information in function notation?
(d) Ebony’s bank balance remained at $0 from Day 12 through Day 15. As you count segments from the left, which segment on the graph1, 2, 3, 4, 5, or 6 represents that information? Explain how you know.
2. Ebony’s bank balance first reached $400 on Day 4. The last day her balance was $400 was Day 8.
(a) Determine . Explain how you determined these amounts.
(b) Estimate . Explain how you determined these amounts.
(c) Jade said that the amount of money Ebony took out of her account each day between Day 8 and Day 12 was the same amount of money she put into her account each day between Day 0 and Day 4. Recall that Day 12 is when the balance first reached $0. Without doing any calculations, how could you show Jade why that cannot be true?
3. On Day 16, Ebony deposited $100 into her account. On each day after Day 16, segment 5, Ebony made a deposit, and those deposits were equal to each other.
(a) Explain how you can determine, just by looking at the graph, whether the amounts she deposited after Day 16 were each less than $100, $100, or more than $100.
(b) Use the graph to estimate in hundreds. Explain how you determined this estimate. Then show how you can estimate the amount of money Ebony deposited into her account each day after Day 16