Question

Identify which of the following functions is proportional.(1 point)
Responses

y=x+12
y equals x plus Start Fraction 1 over 2 End Fraction

y=x2
y equals x squared

y=12x
y equals Start Fraction 1 over 2 End Fraction x

y=12x
y equals Start Fraction 1 over 2 x End Fraction

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 the graph of the function is a straight line passing through the origin (0,0).

Let's analyze the given functions:

1. \( y = x + 12 \) - This is not proportional because it does not pass through the origin (when \( x = 0 \), \( y = 12 \)).

2. \( y = x + \frac{1}{2} \) - This is also not proportional because it does not pass through the origin (when \( x = 0 \), \( y = \frac{1}{2} \)).

3. \( y = x^2 \) - This is not proportional because it is a quadratic function and does not have the form \( y = kx \).

4. \( y = \frac{1}{2}x \) - This is proportional because it can be expressed in the form \( y = kx \) with \( k = \frac{1}{2} \). It passes through the origin.

5. \( y = 12x \) - This is also proportional because it can be expressed in the form \( y = kx \) with \( k = 12 \). It passes through the origin.

Thus, the proportional functions from the list are:
- \( y = \frac{1}{2}x \)
- \( y = 12x \)

Both of these functions are proportional.