Given the parent function , write the equation of the transformed function after a vertical compression by a factor of and a shift up by 6 units. The transformed function is .
Answer & Analysis
Analysis
Question Analysis
This question tests the student's understanding of vertical transformations of functions, specifically vertical compression and vertical shift.
Key Concept Explanation
The general form of a transformed function is given by . For this problem, we focus on the vertical compression (affecting the y-coordinates) and the vertical shift.
Step-by-step Solution
1. Identify the parent function: .
2. Apply the vertical compression by a factor of : Multiply the function by
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