Analyze graph transformations across radical, rational, exponential, logarithmic, and other functions; recognize even and odd functions.
Identify graph features after inside and outside additions in a transformed function
Problem
For \(y~=~\sqrt{x~+~2}~-~3\), state the endpoint and domain.
Big Picture
What this problem is really about
For a transformed square-root function, the endpoint provides both a geometric anchor and the boundary of the domain. Rewrite the inside expression in standard shift form to control its sign, then move the parent endpoint using the inside and outside changes. Confirm the allowed side independently by requiring the radicand to be nonnegative.
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