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Concept

Reflection of a Function

A reflection of a function is a transformation that flips a graph over some line. This line is called the line of reflection and is commonly either the x- or y-axis. A reflection in the x-axis is achieved by changing the sign of the y-coordinate of every point on the graph.
The y-coordinate of all x-intercepts is 0. Thus, changing the sign of the function value at x-intercepts makes no difference — any x-intercepts are preserved when a graph is reflected in the x-axis.
Reflecting a Function in the x-axis
A reflection in the y-axis is instead achieved by changing the sign of every input value.
When x=0, which is at the y-intercept, this reflection does not affect the input value. Therefore, the y-intercept is preserved by reflections in the y-axis.
Reflecting a Function in the y-axis

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