even function
A function y = f(x) is even when f (-x) = f(x) for each x in the domain of f.
An even function is a mathematical function that exhibits a certain symmetry property with respect to the y-axis of a coordinate system. Specifically, an even function is one that satisfies the following condition:
f(-x) = f(x) for all values of x
In other words, if you reflect the graph of an even function across the y-axis, the resulting graph is exactly the same as the original graph. Geometrically, this means that an even function is symmetric about the y-axis.
One example of an even function is the cosine function. If you graph the cosine function, you’ll notice that it oscillates between a maximum value of 1 and a minimum value of -1, with the mid-point of each oscillation occurring at x = 0. Since the cosine function satisfies the evenness condition we stated above, we know that it is an even function.
Even functions are important in mathematics and physics because they naturally arise in many contexts where symmetry is present. For example, in many physical processes, the behavior of a system may be the same whether time is moving forwards or backwards. This is known as time-reversal symmetry, and it can often be represented mathematically using even functions.
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