Question
Which of the following tables represents a function that is proportional? Function 1: x y 1 2 2 4 3 6 Function 2: x y 1 2 2 3 3 4 (1 point) Function is proportional.
Answers
GPT-4o mini
To determine which of the given tables represents a function that is proportional, we need to check if the ratio of \( y \) to \( x \) is constant for each function.
**Function 1:**
- For (1, 2): \( \frac{y}{x} = \frac{2}{1} = 2 \)
- For (2, 4): \( \frac{y}{x} = \frac{4}{2} = 2 \)
- For (3, 6): \( \frac{y}{x} = \frac{6}{3} = 2 \)
In Function 1, the ratio \( \frac{y}{x} \) is constant (equal to 2) for all pairs. This indicates that Function 1 is proportional.
**Function 2:**
- For (1, 2): \( \frac{y}{x} = \frac{2}{1} = 2 \)
- For (2, 3): \( \frac{y}{x} = \frac{3}{2} = 1.5 \)
- For (3, 4): \( \frac{y}{x} = \frac{4}{3} \approx 1.33 \)
In Function 2, the ratios are not constant:
1. \( \frac{y}{x} = 2 \)
2. \( \frac{y}{x} = 1.5 \)
3. \( \frac{y}{x} \approx 1.33 \)
This indicates that Function 2 is not proportional.
**Conclusion:**
Function 1 is the only function that represents a proportional relationship.
**Function 1:**
- For (1, 2): \( \frac{y}{x} = \frac{2}{1} = 2 \)
- For (2, 4): \( \frac{y}{x} = \frac{4}{2} = 2 \)
- For (3, 6): \( \frac{y}{x} = \frac{6}{3} = 2 \)
In Function 1, the ratio \( \frac{y}{x} \) is constant (equal to 2) for all pairs. This indicates that Function 1 is proportional.
**Function 2:**
- For (1, 2): \( \frac{y}{x} = \frac{2}{1} = 2 \)
- For (2, 3): \( \frac{y}{x} = \frac{3}{2} = 1.5 \)
- For (3, 4): \( \frac{y}{x} = \frac{4}{3} \approx 1.33 \)
In Function 2, the ratios are not constant:
1. \( \frac{y}{x} = 2 \)
2. \( \frac{y}{x} = 1.5 \)
3. \( \frac{y}{x} \approx 1.33 \)
This indicates that Function 2 is not proportional.
**Conclusion:**
Function 1 is the only function that represents a proportional relationship.