even function
f(-x) = -f(x), symmetric about the y-axis, tan, cot, csc
An even function is a function in mathematics that is symmetric about the y-axis. In other words, if we reflect the graph of the function across the y-axis, we get the same graph. Mathematically, an even function is defined as:
f(x) = f(-x)
This means that the value of the function at some point x is the same as the value of the function at the opposite point -x. Examples of even functions include:
– f(x) = x^2
– f(x) = cos(x)
– f(x) = |x|
Notice that for each of these functions, replacing x with -x in the function definition gives the same equation as the original. Even functions have some useful properties, such as the fact that the integral of an even function over a symmetrical interval is equal to twice the integral of the function over only half of the interval.
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