Which of the following tables represents a function that is proportional? Function 1:

Question

x y
1 2
2 4
3 6
Function 2:
x y
1 2
2 3
3 4 (1 point)

Function() is proportional.

Answer 1

A function is considered proportional if it can be expressed in the form \( y = kx \), where \( k \) is a constant. This means that for every value of \( x \), the value of \( y \) must be a constant multiple of \( x \).

• Function 1:

  • \( x = 1 \), \( y = 2 \) (Ratio \( \frac{y}{x} = 2 \))
  • \( x = 2 \), \( y = 4 \) (Ratio \( \frac{y}{x} = 2 \))
  • \( x = 3 \), \( y = 6 \) (Ratio \( \frac{y}{x} = 2 \))

  In Function 1, the ratio \( \frac{y}{x} \) is always 2, which means this function is proportional.

• Function 2:

  • \( x = 1 \), \( y = 2 \) (Ratio \( \frac{y}{x} = 2 \))
  • \( x = 2 \), \( y = 3 \) (Ratio \( \frac{y}{x} = 1.5 \))
  • \( x = 3 \), \( y = 4 \) (Ratio \( \frac{y}{x} = \frac{4}{3} \approx 1.33 \))

  In Function 2, the ratios are not constant. Therefore, this function is not proportional.

Conclusion: Function 1 is proportional.