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?
days 10
9. What is the value of c(10) - c(3)
c(10) = 15
c(3) = 5
=10
To find the answers to the questions related to the given piecewise function, follow the steps mentioned below:
1. What are the various prices of tickets?
The prices of tickets are $5, $3 + x, and $15.
2. Which does the 8th day fit in?
The 8th day falls in the range 5 ≤ x < 10.
3. How much would the ticket be on the 8th day?
The ticket price on the 8th day would be:
c(8) = 3 + 8 = $11
4. Which domain does the 5th day fit in? How much would the ticket be?
The 5th day falls in the range 1 ≤ x < 5.
The ticket price on the 5th day would be:
c(5) = $5
5. What does c(3) mean?
c(3) represents the ticket price on the 3rd day, which is $5.
6. What days do the tickets cost $20?
The ticket prices never reach $20 according to the given function. The highest price is $15.
7. What would be the cheapest day(s) to buy a ticket?
The cheapest day(s) to buy a ticket would be when the price is $5, which is on the first day.
8. What is the most expensive day(s) to buy a ticket?
The most expensive day(s) to buy a ticket would be on day 10 when the price is $15.
9. What is the value of c(10) - c(3)?
To find c(10) - c(3), we substitute the values into the function:
c(10) = $15 and c(3) = $5.
Therefore, c(10) - c(3) = $15 - $5 = $10.