Given the parent function , the equation of the function after a vertical stretch by a factor of 4 and a shift down by 2 units is .
Answer & Analysis
Analysis
Question Analysis
This question tests the student's understanding of vertical transformations of functions, specifically vertical stretches and shifts.
Key Concept Explanation
The general form of a transformed function is . Here, represents the vertical stretch or compression, and represents the vertical shift.
Step-by-step Solution
1. Identify the vertical stretch: The factor of 4 means , so the function becomes .
2. Apply the vertical shift: The shift down by 2 units means
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