To model the situation where your sister is buying tickets for a Taylor Swift concert, we need to consider both the ticket cost and the transaction fee. Each ticket costs $55.00, and there is a $5.00 transaction fee for each ticket purchased.
Let \( x \) represent the number of tickets purchased. Therefore, the total cost function \( f(x) \) can be expressed as follows:
- The cost of the tickets is \( 55.00x \) (where \( x \) is the number of tickets).
- The total transaction fee for \( x \) tickets is \( 5.00x \).
So, the total cost function \( f(x) \) combining both the ticket costs and the transaction fees would be:
\[ f(x) = 55.00x + 5.00x \]
This simplifies to:
\[ f(x) = 60.00x \]
However, based on the options provided, we need to find the closest match.
Reviewing the provided options:
- a \( f(x) = 5.00 + 55.00x \)
- b \( f(x) = 55.00 + 5.00x \)
- c \( f(x) = 55.00x \)
- d \( f(x) = 5.00x \)
The function that correctly represents the total cost, including both the ticket price and the transaction fee per ticket, is:
None of the options directly match the standard function format we calculated.
However, if we consider a single ticket purchase (where \( x = 1 \)), the closest viable function from the options given might be a \( f(x) = 5.00 + 55.00x \), since it captures the base cost (the ticket fee plus the transaction fee for at least one ticket) but does not show multiple tickets correctly.
For multiple ticket purchases, neither function accurately depicts the scenario based on normal assumptions unless it assumes that there is always a transaction fee along with the ticket price, in which case the defined function originally stated would apply:
In conclusion, the best function based on your criteria, considering the base cost and dependent on the number of tickets, is:
\[ f(x) = 60.00x \text{ (not listed)} \]
But if you must choose one from the list for a single ticket with transaction fee, option a \( f(x) = 5.00 + 55.00x \) could represent the situation better in that one-case context.