In the scenario given, the cost function is defined as \( C = 50x \), where \( x \) represents the number of participants. Here are the considerations for the possible inputs (domain values) for this function:
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-20: Not a valid input. You cannot have a negative number of participants.
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25: Valid input. This represents 25 participants, leading to a total cost of \( C = 50 \times 25 = 1250 \).
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10.5: Not a valid input. Participants must be a whole number; you cannot have half a participant.
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0: Valid input. This represents a scenario where there are no participants, resulting in a cost of \( C = 50 \times 0 = 0 \).
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50 3/4: Not a valid input. Similar to 10.5, you cannot have a fraction of a participant.
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100: Valid input. This represents 100 participants, leading to a total cost of \( C = 50 \times 100 = 5000 \).
Summary of Selected Values:
- Valid inputs (domain values) for this scenario are 0, 25, and 100.
- I chose these values because:
- The input must be a non-negative integer (whole number) since you cannot have a negative number of participants or a fraction of a participant in this context.
- Hence, values like -20, 10.5, and 50 3/4 are not possible. Only whole numbers greater than or equal to zero are acceptable as inputs for the function.