Given the function , write the equation of the function after it is reflected over the y-axis, stretched vertically by a factor of 3, and then shifted 2 units up. The transformed function is.
Answer & Analysis
Analysis
Question Analysis
This problem assesses the ability to apply multiple transformations (reflection, vertical stretch, and vertical shift) to a polynomial function.
Key Concept Explanation
Reflections over the y-axis are represented by . Vertical stretches are represented by , where stretches the graph. Vertical shifts are represented by , where shifts the graph up and shifts the graph down.
Step-by-step Solution
1. Reflect the function over the y-axis:
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