2. 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.
A) 50
B) 80
C) 210
D) 150
E) 0

3. 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 number of students (x) and your output is the total cost (C)

1. Select all the possible Inputs (Domain values) for the cost function, and then explain why you chose those values.
A) 25
B) 50 3/4
C) 100
D) 0
E) -20
F) 10.5

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
4 hours ago

Question 1: Possible Outputs (Range Values)

The cost function is given by \( C = 50x \), where \( x \) is the number of participants and \( C \) is the total cost. The output \( C \) must be a non-negative multiple of 50 since each participant contributes $50 to the total cost.

Possible outputs (Range values):

  • A) 50 → Valid output: This corresponds to 1 participant (C = 50 × 1).
  • B) 80 → Invalid output: $80 is not a multiple of $50.
  • C) 210 → Invalid output: $210 is not a multiple of $50.
  • D) 150 → Valid output: This corresponds to 3 participants (C = 50 × 3).
  • E) 0 → Valid output: This corresponds to 0 participants (C = 50 × 0).

Chosen values explanation: The valid outputs are those that can be reached by multiplying the participant fee ($50) by a non-negative integer (the number of participants). Therefore, the possible outputs (range values) are A) 50, D) 150, and E) 0, as these represent valid costs based on the number of participants.

Question 2: Possible Inputs (Domain Values)

The cost function is again given by \( C = 50x \), where \( x \) is the number of participants. The value of \( x \) must be a non-negative integer, as you cannot have a negative number of participants or a fraction of a participant in this context.

Possible inputs (Domain values):

  • A) 25 → Valid input: Represents 25 participants.
  • B) 50 3/4 → Invalid input: Represents a fraction of a participant, which is not allowed.
  • C) 100 → Valid input: Represents 100 participants.
  • D) 0 → Valid input: Represents no participants.
  • E) -20 → Invalid input: Negative number of participants is not possible.
  • F) 10.5 → Invalid input: Represents a fraction of a participant.

Chosen values explanation: The valid inputs are non-negative integers, as they represent the number of participants. Therefore, the possible inputs (domain values) are A) 25, C) 100, and D) 0. All other options are either negative or fractional, which do not represent a valid count of participants.