Question
Number of Tickets Purchased Price Per Ticket ($)
0–5 35.75
6–10 30.50
11 or more 25.25
Grace and her friends are planning a trip to the amusement park. The table includes the prices for tickets, which are dependent upon how many are purchased. Which of the following options includes the piecewise function that represents the given problem, where f(x)
represents the cost per ticket, and x represents the number of tickets purchased?
Option #1: f(x)=⎧⎩⎨⎪⎪35.75,30.50,25.25, 1≤x≤56<x≤10x>11
Option #2: f(x)=⎧⎩⎨⎪⎪35.75,30.50,25.25, 1≤x≤56≤x≤10x≥11
Option #3: f(x)=⎧⎩⎨⎪⎪35.75,30.50, 25.25,x≥56≤x≤10x≥11
(1 point)
The problem can be represented by the piecewise function in Option #
Answers
GPT-4o mini
To define a piecewise function that represents the problem, we need to use the correct intervals for the number of tickets purchased and their corresponding prices.
According to the pricing structure:
- For 0 to 5 tickets, the price is $35.75.
- For 6 to 10 tickets, the price is $30.50.
- For 11 or more tickets, the price is $25.25.
Thus, the correct piecewise function should be structured as follows:
\[
f(x) =
\begin{cases}
35.75 & \text{if } 0 \leq x \leq 5 \\
30.50 & \text{if } 6 \leq x \leq 10 \\
25.25 & \text{if } x \geq 11
\end{cases}
\]
Now, we can evaluate the given options:
- **Option #1**: This option does not have the correct intervals and uses "1≤x≤5" which implies something different than what is given.
- **Option #2**: This option uses "1≤x≤5" which is incorrect.
- **Option #3**: This option also incorrectly states the intervals.
Since none of the options provided correctly represent the piecewise function based on the table, I would advise you to select the option that most closely resembles the structure of the piecewise function. However, based on a strict interpretation of the intervals and conditions provided, none of them are correct.
It looks like there might have been a misunderstanding in the options given, or possibly an error in transcribing the problem. If you are looking for the closest option with the correct interval, please review the available choices again or give more context.
According to the pricing structure:
- For 0 to 5 tickets, the price is $35.75.
- For 6 to 10 tickets, the price is $30.50.
- For 11 or more tickets, the price is $25.25.
Thus, the correct piecewise function should be structured as follows:
\[
f(x) =
\begin{cases}
35.75 & \text{if } 0 \leq x \leq 5 \\
30.50 & \text{if } 6 \leq x \leq 10 \\
25.25 & \text{if } x \geq 11
\end{cases}
\]
Now, we can evaluate the given options:
- **Option #1**: This option does not have the correct intervals and uses "1≤x≤5" which implies something different than what is given.
- **Option #2**: This option uses "1≤x≤5" which is incorrect.
- **Option #3**: This option also incorrectly states the intervals.
Since none of the options provided correctly represent the piecewise function based on the table, I would advise you to select the option that most closely resembles the structure of the piecewise function. However, based on a strict interpretation of the intervals and conditions provided, none of them are correct.
It looks like there might have been a misunderstanding in the options given, or possibly an error in transcribing the problem. If you are looking for the closest option with the correct interval, please review the available choices again or give more context.