Consider the following scenario. The fee for an upcoming science camp is $50 per participant. The total cost of the camp, in dollars, is a function of the number of participants. `C=50x` where your input is the number of students (x) and your output is the total cost (C) 1. Select all the possible outputs (Range values) for the cost function, and then explain why you chose those values. (3 points) Responses 210 210 150 150 0 0 80 80 50

To determine the possible outputs (range values) for the cost function \( C = 50x \), where \( x \) is the number of participants, let's analyze the function.

1. Understanding the function: The cost \( C \) increases in increments of $50 as the number of participants \( x \) increases. Therefore, \( C \) depends directly on how many participants there are.

2. Valid Inputs (x): Since \( x \) (the number of participants) cannot be negative and must be a whole number (you can't have a fraction of a person), the smallest value for \( x \) is 0, which corresponds to not having any participants.

3. Calculating Costs: For different integer values of \( x \):

   • If \( x = 0 \), then \( C = 50 \times 0 = 0 \)
   • If \( x = 1 \), then \( C = 50 \times 1 = 50 \)
   • If \( x = 2 \), then \( C = 50 \times 2 = 100 \)
   • If \( x = 3 \), then \( C = 50 \times 3 = 150 \)
   • If \( x = 4 \), then \( C = 50 \times 4 = 200 \)
   • If \( x = 5 \), then \( C = 50 \times 5 = 250 \)
   • And so on, producing values of \( 0, 50, 100, 150, 200, 250, \ldots \)

Now, let’s select the outputs from the list provided: 210, 150, 0, 80, 50.

• 0: Valid, since \( C \) can be 0 when \( x = 0 \).
• 50: Valid, since \( C \) can be 50 when \( x = 1 \).
• 150: Valid, since \( C \) can be 150 when \( x = 3 \).
• 80: Invalid, since the function only produces values that are multiples of 50.
• 210: Invalid, since this value is not a multiple of 50.

Final selection of possible outputs (Range values): 0, 50, 150

The reason for selecting these values is that they are all multiples of 50, corresponding to valid scenarios of participant counts (non-negative integers) as governed by the function \( C = 50x \).