The graph of has its lowest point at . What are the coordinates of the highest point or lowest point of the graph of ?
Answer and explanation
Correct answer: D. , a highest point
- Step 1: Replacing by shifts the graph unit left, so the -coordinate becomes .
- Step 2: Multiplying by reflects over the -axis (low point becomes high point) and stretches: .
- Step 3: Adding shifts up: . The point is and it is a highest point.
Answer
, a highest point.
Why not the others: Shifting right instead of left gives ; ignoring the reflection leaves a lowest point with misapplied or .
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