Relate a function's domain to its equation, graph, and context, especially when model choice matters.
Classify why an input is invalid
Problem
How should \(t~=~-2~\text{seconds}\) be classified for this polynomial height-after-launch model?
Big Picture
What this problem is really about
Test invalidity in two stages instead of treating every rejected input as an algebra problem. First ask whether substitution produces a real polynomial value; then compare the input with the elapsed-time boundary established by the word after. This separates a formula restriction from an otherwise valid number that the physical story does not permit.
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