Question

Which of the following tables represents a function that is proportional?
Function 1:
xy
12
24
36
Function 2:
xy
12
23
34
(1 point)

Answer 1

To determine if a table represents a function that is proportional, we need to check if there is a constant ratio (k) between the x and y values for each pair of (x, y) coordinates.

For Function 1:
- When x = 1, y = 2, the ratio \( k = \frac{2}{1} = 2 \)
- When x = 2, y = 4, the ratio \( k = \frac{4}{2} = 2 \)
- When x = 3, y = 6, the ratio \( k = \frac{6}{3} = 2 \)

Since the ratio \( k \) is constant at 2, Function 1 is proportional.

For Function 2:
- When x = 1, y = 2, the ratio \( k = \frac{2}{1} = 2 \)
- When x = 2, y = 3, the ratio \( k = \frac{3}{2} = 1.5 \)
- When x = 3, y = 4, the ratio \( k = \frac{4}{3} \approx 1.33 \)

Since the ratios are not constant in Function 2, it is not proportional.

**Conclusion:** Function 1 represents a function that is proportional.