Understanding the Reflection Property of Functions: Explained through an Example

Function f(-x) is a reflection of f(x)

Function f(-x) is a reflection of f(x) over the y-axis

Function f(-x) is a reflection of f(x) over the y-axis.

To understand why this is the case, let’s break it down.

Consider a point (x, y) on the graph of f(x).
When we evaluate f(-x), we are substituting -x into the function. Therefore, we have f(-x) = y, which means that the corresponding point on the graph of f(-x) is (-x, y).

Now, if we compare the original point (x, y) with the corresponding point (-x, y), we can see that they have the same y-coordinate but opposite x-coordinates. This means that the points lie on the same horizontal line, but on opposite sides of the y-axis.

Since every point on the graph of f(x) has a corresponding point on the graph of f(-x) with the same y-coordinate but opposite x-coordinate, we can conclude that f(-x) is a reflection of f(x) over the y-axis.

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