Given the function , write the equation of the function after shifting it 2 units up and then reflecting it over the y-axis: ______ .
Answer & Analysis
Analysis
Question Analysis
This problem assesses the student's ability to apply multiple transformations (vertical shift and reflection over the y-axis) to a polynomial function.
Key Concept Explanation
A vertical shift by units is represented by the transformation , and a reflection over the y-axis is represented by the transformation . For this problem, we need to first shift the function 2 units up and then reflect it over the y-axis.
Step-by-step Solution
1. Start with the original function:
2. Apply the vertical shift:
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