The amount in Ebony’s bank account B d( ) 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 information given, as well as your general knowledge of graphs of functions.

Ebony kept her bank account open for only 3 weeks. The graph shows the entire 3 weeks. During that time, her greatest balance was $400.

(1) Give the domain and range of the function.

(2) Give an estimate to the nearest hundreds for B(0) . Explain how you determined your estimate and what B(0) means in the context of this 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.

1)

Domain:

Range:

2)

On Day 0, the day Ebony opened her account, she made an initial deposit of $200.

3)

4)

The 4th Segment.

Step-by-step explanation:

We are given the graph of the amount of money B(d) in Ebony's bank account after d days.

We know that Ebony kept her bank account open for only 3 weeks. During that time, the greatest balance was $400.

Let's answer each of the questions using the graph and the available information.

Part 1)

The domain is the span of x-values our function covers.

In this case, our domain is dealing with days.

We know that Ebony opened her account for 3 weeks, or 21 days.

Note that our domain cannot be negative because, say, Day -1 makes no sense in this context.

The maximum value of our domain is 21 Days because she only opened her account for 3 weeks.

So, our domain will be all numbers between 0 and 21 (we include the 0 because the day she opened her account is Day 0).  

So, our domain is, as a compound inequality:

The range is the span of y-values our function covers.

In this case, the range is dealing with the account balance.

We know that the greatest amount of money Ebony had in her account was $400.

Although her balance can technically be negative, this isn't shown on the graph. So, we're assuming that she always had a $0 or positive balance.

So, our range is all numbers between 0 and 400. As a compound inequality, this is:

Part 2)

We know that the greatest amount of money Ebony had in her account was $400.

So, the highest y-value is 400. We can see that this is the second segment represented by the second and third points.

B(0), the first point, seems to halfway between 0 and 400.

Therefore, it is a reasonable estimate to say that B(0) is 400/2 or $200.

This means that on Day 0, the day Ebony opened her account, she made an initial deposit of $200.

Part 3)

We are given that Ebony's balance first reached $0 on Day 12.

So, on Day 12, our d is 12.

And our B(d) is 0. Therefore, by substituting d for 12, we can write:  

Part 4)

If the bank balance is $0, this means that the segment must be completely flat and it must lay on the x-axis.

It must lay on the x-axis because when the bank balance is $0, our y or B(d) is also 0, and this happens at the x-axis.

So, counting from the left, the segment where the balance is $0 is segment 4.

This is almost invisible, but, as we know, it's there, it's just that it's 0.

And we're done!