To determine which table represents a non-proportional function, we need to understand the difference between proportional and non-proportional relationships. A proportional relationship means that the ratio of \( y \) to \( x \) is constant. For a function to be non-proportional, this ratio must change as \( x \) changes.
Let's analyze the two functions:
Function 1:
- When \( x = 3, y = 10 \) => Ratio \( \frac{y}{x} = \frac{10}{3} \approx 3.33 \)
- When \( x = 5, y = 25 \) => Ratio \( \frac{y}{x} = \frac{25}{5} = 5 \)
- When \( x = 8, y = 34 \) => Ratio \( \frac{y}{x} = \frac{34}{8} = 4.25 \)
Since the ratios are different for different \( x \) values, Function 1 is non-proportional.
Function 2:
- When \( x = 2, y = 10 \) => Ratio \( \frac{y}{x} = \frac{10}{2} = 5 \)
- When \( x = 5, y = 25 \) => Ratio \( \frac{y}{x} = \frac{25}{5} = 5 \)
- When \( x = 9, y = 45 \) => Ratio \( \frac{y}{x} = \frac{45}{9} = 5 \)
Since the ratio is constant (5) across all pairs, Function 2 is proportional.
Conclusion:
Function 1 is non-proportional.
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