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[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

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[PIVOT]

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The maximum breeding capacity of a fish population in a fishery is \( m \) tons. To ensure adequate space for the fish to grow, the actual breeding capacity cannot reach the maximum, and a suitable amount of space must be reserved. The annual growth of the fish population, \( y \) tons, is directly proportional to the product of the actual breeding capacity, \( x \) tons, and the free rate. The proportionality constant is \( k \) (where \( k > 0 \), and the free rate is the ratio of the free capacity to the maximum breeding capacity).
1. Write the functional relationship of \( y \) with respect to \( x \), and identify the domain of this function.
2. Find the maximum annual growth of the fish population and determine the range of \( k \) at this maximum.

Present the answer in LaTex format: \boxed{Your answer}
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