Below is a function the represents the sales for tickets to battle of the Bands Phoenix Music Festival. Student council needs students to buy ticket early in order to book a venue. In order to do this they made a piece scale as follows, where x is the days since February 10th.
Piecewise function
c(x) =
5; 1<= x <5
3 + x; 5<x<=10
15; x =>10
Basic questions:
1. What are the various prices of tickets?
= 5, 3 +x, 15
2. Which does the 8th day fit in?
5<=x <10
3. How much would the ticket be on the 8th day?
= 3+8
= 11
4. Which domain does the 5th day fit in? How much would the ticket be?
5. What does c(3) mean?
c(3) = $5
6. What day’s do the ticket cost $20? Never b/c the highest is 15.
7. What would be the cheapest day(s) to buy a ticket?
8. What is the most expensive day(s) to buy a ticket?
9. What is the value of c(10) - c(3)
c(10) = 15
c(3) = 5
=10
1. The various prices of tickets are:
- For 1<= x < 5 days: $5
- For 5<x <= 10 days: $3 + x
- For x >= 10 days: $15
2. The 8th day fits in the range 5<= x < 10.
3. On the 8th day, the ticket price would be:
c(8) = 3 + 8 = $11
4. The 5th day fits in the range 1<= x < 5. Therefore, the ticket price on the 5th day is $5.
5. c(3) represents the price of the ticket on the 3rd day. Therefore, c(3) = $5.
6. There are no days on which the ticket cost $20. The highest price mentioned in the function is $15.
7. The cheapest day(s) to buy a ticket would depend on the function. However, from the given function, the price of $5 on the 1st day appears to be the cheapest.
8. The most expensive day(s) to buy a ticket would be on or after the 10th day, as the price is fixed at $15.
9. To find the value of c(10) - c(3), we need to substitute the values of c(10) and c(3) from the given function:
c(10) = 15
c(3) = 5
Therefore, c(10) - c(3) = 15 - 5 = 10.