reflection across the x-axis
f(x) = – (x³)
Reflection across the x-axis is a transformation in which each point in a figure is flipped or reflected over the x-axis. The x-axis is the horizontal line that divides the coordinate plane into two halves, with positive values above the x-axis and negative values below the x-axis.
To perform a reflection across the x-axis, you need to follow these steps:
1. Draw the original figure and the x-axis in the coordinate plane.
2. Identify the points in the figure that are located above the x-axis.
3. Replace the y-coordinate of each point with its negative value to get the reflection of the point over the x-axis.
4. Plot the new points to draw the reflected figure.
For example, let’s consider the point (3, 4) on a coordinate plane. To reflect this point across the x-axis, we replace the y-coordinate 4 with its negative value -4. Thus, the reflection of (3, 4) over the x-axis is (-3, -4).
In general, all the points that are above the x-axis will move below it when they are reflected across the x-axis, and the points that are below the x-axis will move above it. The x-coordinates of the points, however, remain the same after the reflection.
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