Bot GPT 4-o mini A function is considered proportional if it can be expressed in the form \( y = kx \), where \( k \) is a constant. In other words, there should be a constant ratio between \( y \) and \( x \).
Let's evaluate the provided options:
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\( y = \frac{1}{2}x \): This is in the form \( y = kx \) where \( k = \frac{1}{2} \). This function is proportional.
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\( y = \frac{1}{2} x \): This is the same as the first option, thus it is also in the form \( y = kx \) where \( k = \frac{1}{2} \). This function is proportional.
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\( y = x + \frac{1}{2} \): This function cannot be expressed in the form \( y = kx \) because of the constant \( \frac{1}{2} \) added to \( x \). Thus, it is not proportional.
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\( y = x^2 \): This function is not in the form \( y = kx \), as it is a quadratic function. Thus, it is not proportional.
In summary, the functions that are proportional are:
- \( y = \frac{1}{2}x \)
- \( y = \frac{1}{2} x \)
Both of these options exhibit proportionality.
1 answer