Question

Function applications? (Question in the comments)

Answer 1

Ebony's bank account B(d) is the function of the number of (d) days since the account has been opened. The graph shows segments that represent her daily bank balance.
Note: Her bank account was open for a span of three weeks and the greatest balance she had was $400.
Part one:
1) Domain and range of the function.
2) Give an estimate to the nearest hundreds for B(0). Explain how you determined your estimate and tell what B(0) means in context of the situation.
3) Ebony’s bank balance first reached $0 on Day 12. How would you show that information in function notation?
4) Ebony’s bank balance remained at $0 from Day 12 through Day 15. As you count segments from the left, which segment on the graph 1, 2, 3, 4, 5, or 6 represents that information? Explain how you know.
Part two:
Note: Her bank account had reached $400 on day four. The last day the balance was $400 was day eight.
1) Determine B(5), B(6), B(7)
2) Determine B(1), B(2), B(3)
3) 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?
Part three:
Note: 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.
1) 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.
2) Use the graph to estimate B(21) in hundreds.

I don't want the answers per se, I just want to know how to get them. If you could explain that, that'd be great, thank you!