Answer:
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!