To determine the possible outputs (range values) for the cost function \( C = 50x \), we first need to understand that \( x \) represents the number of participants, and it cannot be negative. The number of participants must also be a whole number (since you can't have a fraction of a participant).
Given the formula:
- If \( x = 0 \): \( C = 50 \times 0 = 0 \)
- If \( x = 1 \): \( C = 50 \times 1 = 50 \)
- If \( x = 2 \): \( C = 50 \times 2 = 100 \)
- If \( x = 3 \): \( C = 50 \times 3 = 150 \)
- If \( x = 4 \): \( C = 50 \times 4 = 200 \)
- And so on...
The outputs of the function \( C \) are multiples of 50, which means they can be represented as \( 0, 50, 100, 150, 200, \) etc.
Now, let's analyze the options provided: A. 0 - Valid (when \( x = 0 \)) B. 50 - Valid (when \( x = 1 \)) C. 80 - Invalid (not a multiple of 50) D. 210 - Invalid (not a multiple of 50) E. 150 - Valid (when \( x = 3 \))
Based on this reasoning, the valid outputs (range values) for the cost function \( C = 50x \) are A (0), B (50), and E (150).
I chose these values because they correspond to valid inputs (whole non-negative numbers of participants) that result in an output calculated as \( C = 50x \). Values that do not align with this relationship, such as 80 and 210, are excluded from the range.