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Identify a parent family and domain from invariant shape
Problem
Identify the parent family and domain from this complete shape description: The graph has \(\text{one}~\text{included}~\text{endpoint}\) at \((0,0)\), has \(\text{no}~\text{points}\) left of it, and is a curved branch continuing right.
Parent families have invariant shape clues that survive changes of scale. We’ll look first for one-sided versus two-sided extent, then distinguish a curved endpoint branch from a V, an S-curve, or jumps, and derive the domain from the graph’s horizontal reach and endpoint status.
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