The relationship between \( y = f(x) \) and \( y = f(-x) \) is called a reflection transformation. Specifically, it is a reflection over the y-axis on a graph. This means that every point of the graph of \( y = f(-x) \) is a mirror image of the corresponding point of the graph of \( y = f(x) \) across the y-axis.
In more detail, if the point \( (a, b) \) is on the graph of \( y = f(x) \) (meaning \( f(a) = b \)), then the point \( (-a, b) \) will be on the graph of \( y = f(-x) \), since \( f(-a) = b \). Thus, the graph of \( f(-x) \) can be seen as flipping the graph of \( f(x) \) around the y-axis.
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