An even function is a type of mathematical function that exhibits symmetry about the y-axis. This means that for any input value x , the output remains the same when the input is negated. In mathematical terms, a function f(x) is considered even if f(-x) = f(x) for all x in its domain. Common examples of even functions include polynomial functions with even degrees, such as x^2 and x^4 . Even functions can be visually identified on a graph, as their left and right halves mirror each other across the y-axis. This property makes them useful in various areas of mathematics, including calculus and Fourier analysis. Understanding even functions helps in solving equations and analyzing the behavior of different types of functions.