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)

Question

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 #
.

Answer 1

Based on the descriptions given in options, we can analyze the structure of each option for the piecewise function representing the ticket prices based on the number of tickets purchased (x).

1. The range for each price point should correspond logically with how the prices are set according to the number of tickets.
2. The correct piecewise function is one that reflects the specific ranges for each given cost per ticket.

Let's clarify the likely structure of ticket prices:

• $35.75 for 1 to 5 tickets
• $30.50 for 6 to 10 tickets
• $25.25 for 11 or more tickets

Now let's evaluate each option:

Option #1:
f(x)=
⎧⎩⎨⎪⎪
35.75, 1≤x≤5
30.50, 6<x≤10
25.25, x>11

This option is incorrect because it has an inconsistency with the intervals particularly for 6 and 11.

Option #2:
f(x)=
⎧⎩⎨⎪⎪
35.75, 1≤x≤5
30.50, 6≤x≤10
25.25, x≥11

This option is correct given that:

• $35.75 applies to 1 to 5 tickets (1 ≤ x ≤ 5)
• $30.50 applies to 6 to 10 tickets (6 ≤ x ≤ 10)
• $25.25 applies to 11 or more tickets (x ≥ 11)

Option #3:
f(x)=
⎧⎩⎨⎪⎪
35.75, x≥5
30.50, ≤x≤10
25.25, x≥11

This option is incorrect as the first price point doesn't correctly constrain the values.

Based on this analysis, the correct option that represents the piecewise function for the ticket prices is:

Option #2: f(x)=⎧⎩⎨⎪⎪35.75, 1≤x≤5 30.50, 6≤x≤10 25.25, x≥11**.