Analyze graph transformations across radical, rational, exponential, logarithmic, and other functions; recognize even and odd functions.
Read signed horizontal and vertical shifts and verify an anchor
Problem
For \(\sqrt{x~-~4}~+~7\), state \(h\) and \(k\), describe the horizontal and vertical shifts, and map the parent endpoint \((0,~0)\).
Big Picture
What this problem is really about
Read transformations from standard form, treating input changes and output changes differently. An expression inside the function moves horizontal coordinates with the opposite visible sign, while an outside addition moves vertical coordinates with its own sign. Map the parent function’s defining anchor to verify both directions instead of trusting a memorized sign rule.
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