Consider the absolute value function . If the graph of this function is reflected over the x-axis and then shifted 3 units to the right, the new function can be written as y = __________.
Answer & Analysis
Analysis
Question Analysis
This question assesses the student's ability to apply multiple transformations to an absolute value function, specifically reflection and horizontal translation.
Key Concept Explanation
Reflecting a function over the x-axis changes the sign of the coefficient in the general form .
Horizontal translation is controlled by the parameter . A positive shifts the graph to the right, while a negative shifts it to the left.
Step-by-step Solution
1. Reflect the function over the x-axis: The coefficient changes from 3 to -3, resulting in
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