A vertical reflection of a graph refers to a transformation that flips the graph across the y-axis. For a function \( f(x) \), the vertical reflection is represented by \( y = -f(x) \).
When you take a vertical reflection, each point \( (x, y) \) on the graph of \( y = f(x) \) will be transformed to the point \( (x, -y) \) on the graph of \( y = -f(x) \). This means that:
- If a point on the original graph is at \( (x, f(x)) \), then the corresponding point on the reflected graph will be at \( (x, -f(x)) \).
- Essentially, the new graph will have the same x-coordinates but the y-coordinates will be the negative of the corresponding y-coordinates from the original graph.
This transformation does not alter the x-coordinates; instead, it flips the values of the function across the x-axis. Thus, if you have a function \( f(x) \), the graph of \( y = -f(x) \) will be an upside-down version of the graph of \( y = f(x) \).
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