To determine the possible outputs (range values) for the cost function \( C = 50x \), we need to analyze the relationship between the number of participants \( x \) and the total cost \( C \).
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Understanding the Function:
- The function \( C = 50x \) indicates that for every participant (x), the cost increases by $50.
- Therefore, if there are zero participants, the cost is $0 (C = 50 * 0 = 0).
- If there is one participant, the cost is $50 (C = 50 * 1 = 50).
- If there are two participants, the cost is $100 (C = 50 * 2 = 100).
- This pattern continues such that the total cost is always a multiple of $50 depending on the number of participants.
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Selecting the Possible Outputs:
- The possible outputs must be non-negative since the cost cannot be negative. Hence, \( C \) can be 0 (if there are zero participants).
- As for other outputs:
- \( 50 \) is a possible output when there is 1 participant.
- \( 80 \) is not a possible output, because it is not a multiple of 50.
- \( 150 \) is a possible output when there are 3 participants (C = 50 * 3).
- \( 210 \) is not a possible output, since it is also not a multiple of 50.
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Conclusion: Based on this analysis, the possible outputs from the given options are:
- 0
- 50
- 150
These outputs are valid because they correspond to the total costs generated by integer values of \( x \) that result in non-negative multiples of 50. Thus, the selected possible outputs (0, 50, 150) reflect the outputs generated from valid integer inputs into the cost function.