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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