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Function domain word problems

Mason stands on the 5th5^\text{th} step of a vertical ladder. The ladder has 1515 steps, and the height difference between consecutive steps is 0.5 m0.5\text{ m}.
h(n)h(n) models the height above the ground of Mason's feet (in m\text{m}) after moving nn steps (if Mason went down the ladder, nn is negative.)
Which number type is more appropriate for the domain of hh?
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What's the appropriate domain?
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