To determine which table represents a non-proportional function, we need to check if the relationship between \( x \) and \( y \) is proportional. A function is proportional if the ratio \( \frac{y}{x} \) is constant for all values of \( x \).
Let's calculate the ratios for both functions:
Function 1:
- For \( (3, 10) \): \( \frac{10}{3} \approx 3.33 \)
- For \( (5, 25) \): \( \frac{25}{5} = 5 \)
- For \( (8, 34) \): \( \frac{34}{8} = 4.25 \)
Since the ratios are not constant, Function 1 is non-proportional.
Function 2:
- For \( (2, 10) \): \( \frac{10}{2} = 5 \)
- For \( (5, 25) \): \( \frac{25}{5} = 5 \)
- For \( (9, 45) \): \( \frac{45}{9} = 5 \)
Since the ratios are all constant (equal to 5), Function 2 is proportional.
Therefore, Function 1 is the non-proportional function.