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.

Answer 1

A function is considered proportional if the relationship between \( x \) and \( y \) can be expressed as \( y = kx \) for some constant \( k \). This means that as \( x \) increases, \( y \) increases in a consistent ratio.

Let's analyze both functions:

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

In Function 1, the ratios of \( y \) to \( x \) are constant (always equal to 2). Therefore, this function is proportional.

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

In Function 2, the ratios of \( y \) to \( x \) are not constant. Therefore, this function is not proportional.

Based on the analysis, **Function 1 is proportional**.