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
To answer these questions about the given piecewise function c(x), let's break it down:
1. The various prices of tickets are:
- For 1 ≤ x < 5, the ticket price is $5.
- For 5 < x ≤ 10, the ticket price is $3 + x.
- For x ≥ 10, the ticket price is $15.
2. The 8th day falls into the range 5 ≤ x < 10.
3. On the 8th day (x = 8), the ticket price would be:
c(8) = 3 + 8 = $11.
4. The 5th day falls into the range 1 ≤ x < 5. Therefore, the ticket price would be:
c(5) = $5.
5. c(3) represents the ticket price on the 3rd day after February 10th, which is $5.
6. The ticket price never reaches $20 because the highest price is $15.
7. To find the cheapest day(s) to buy a ticket, we need to find the minimum price among the different ranges. In this case, the cheapest price is $5, which occurs on the first day, 1 ≤ x < 5.
8. To find the most expensive day(s) to buy a ticket, we need to find the maximum price among the different ranges. In this case, the highest price is $15, which occurs on and after the 10th day, x ≥ 10.
9. The value of c(10) - c(3) can be calculated as follows:
c(10) = $15
c(3) = $5
Therefore, c(10) - c(3) = $15 - $5 = $10.
4. The 5th day fits in the domain 1 <= x < 5, and the ticket price would be $5.
7. The cheapest day(s) to buy a ticket would be on the 1st, 2nd, 3rd, 4th, or 5th day, where the ticket price is $5.
8. The most expensive day(s) to buy a ticket would be on or after the 10th day, where the ticket price is $15.
9. The value of c(10) - c(3) would be $15 - $5 = $10.