After a vertical reflection across the $x$-axis, $f(x)$ is
A. -f(-x)
B. f(x-1)
C. -f(x)
D. f(-x)
Answer (2)
A vertical reflection across the x-axis changes the sign of the function.
The transformed function is represented by − f ( x ) .
Therefore, the answer is − f ( x ) .
Explanation
Understanding Vertical Reflection When a function f ( x ) is reflected vertically across the x-axis, the sign of the function changes. This means that every y -value becomes its opposite.
Applying the Transformation Therefore, the transformed function is − f ( x ) .
Examples
Imagine you are designing a symmetrical building where the top half mirrors the bottom half. If you have a function that describes the shape of the top half, reflecting it vertically across the x-axis (the ground) gives you the shape of the bottom half. This is a practical application of vertical reflection in architecture and design. Understanding function transformations helps in creating symmetrical and balanced designs efficiently.
After a vertical reflection across the x-axis, the function is represented as -f(x). Therefore, the correct answer is option C: -f(x).
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