## what is even function?

### An even function is a mathematical function where the value of the function is the same when the input is replaced by its negation

An even function is a mathematical function where the value of the function is the same when the input is replaced by its negation. In other words, if a function f(x) is even, then f(x) = f(-x) for all x in the domain of the function.

Graphically, an even function is symmetric about the y-axis. This means that if you were to fold the graph of an even function along the y-axis, the shape of the function on one side would match exactly with the shape on the other side.

Even functions typically have the following properties:

1. The y-intercept of an even function lies on the y-axis.

2. If the function has any x-intercepts, they must be symmetrically located with respect to the y-axis.

3. The average rate of change of an even function over any interval containing both negative and positive values of x is zero, since opposite x-values will produce the same function value.

Some examples of even functions include:

– f(x) = x^2

– g(x) = |x|^2 (where |x| denotes the absolute value of x)

– h(x) = cos(x)

It is important to note that not all functions are even. Functions that are not even are called odd functions. Odd functions have the property that f(-x) = -f(x) for all x in their domain.

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