Finding the Equation of a Curve After Reflection in the Line y=k

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The lineis horizontal and reflection in this line turns the graph upside down,

If the curveis reflected in the linethe x – axis, the equation of the reflected curve isbut this is not the case for reflection in any other line.

Ifis reflected in the lineyou can think of any point with coordinate RELATIVE to the linebeing reflected to the pointrelative to that line, orrelative to the x – axis.

The curvethen has equationafter reflection in the line y=k.

Example: The curveis reflected in the line y=0.5.

The above analysis tells us that the equation of the transformed curve will be

Obviously any points on the linewill not be shanged by the reflection. The original curve, the reflection line and the transformed curve are shown in the diagram below.

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