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Reflection over x axis vs y axis equation

The rule for reflecting over the X axis is to negate the value of the y-coordinate of each point, but leave the x-value the same. For example, when

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Reflection across the x-axis: y = -f(x)

The best way to practice drawing reflections over y axis is to do an example problem: Example: Given the graph of y = f (x) y=f(x) y = f (x) as shown, sketch y = f (− x) y = f(-x) y = f (− x). Remember, the only step we have to do before

Reflections

Thus, for every point of an object, the mirror line is perpendicularly bisects the line segment joining the point with its image. reflected in the x-axis. Reflection about x - axis, So replace y by

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Reflections

The formula for this is: {eq}(x,y) \rightarrow (-x,y) {/eq}. To reflect an equation over the y-axis, simply multiply the input variable by -1: {eq}y=f(x) \rightarrow y=f(-x) {/eq}.
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3.3 Graphing Functions Using Reflections about the Axes

The function y = ( x − 6) 2 − 4 has a parabola as its curve. When reflected over the line y = x, the x and y coordinates of all the points lying along the curve will switch their places.

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Reflection Over X-Axis & Y-Axis

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