Tell students that an important aspect of working with functions is defining a domain that makes sense given the context and what we are trying to do. \(D(\text-1)\), however, does not make sense here unless we attempt to define what a “negative dot” is. If students ask about \(D(0)\), let them know that we could say for the pattern that there is a Step 0 with 0 dots. Make sure students understand that non-integer values do not make sense for the sequence represented by this dot pattern since there is no partial step between the steps that we can calculate. The two important takeaways from this discussion are that sequences are a type of function whose domain is a subset of the integers and an understanding of what \(D(n)\) and \(D(n-1)\) mean.īegin the discussion by inviting students to share values that do and do not make sense for \(n\), recording these for all to see.
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