They are special types of functions. A function is "even" when: f (x) = f (−x) for all x. In other words there is symmetry about the y-axis (like a reflection): This is the curve f (x) = x2+1.

Even functions are those real functions whose graph is self-symmetric with respect to the y-axis, and odd functions are those whose graph is self-symmetric with respect to the origin.

A function is an even function if f of x is equal to f of −x for all the values of x. This means that the function is the same for the positive x-axis and the negative x-axis, or graphically, symmetric …

Sep 25, 2025 · Even Functions: An even function remains unchanged when its input is negated (same output for x and -x), reflecting symmetry about the y-axis. Odd Functions: An odd …

Understand whether a function is even, odd, or neither with clear and friendly explanations, accompanied by illustrative examples for a comprehensive grasp of the concept.

4 days ago · Examples of even functions include 1 (or, in general, any constant function), |x|, cosx, x^2, and e^ (-x^2). An even function times an odd function is odd, while the sum or …

Jan 7, 2025 · The even and odd functions are classified by their symmetry properties. A function f is even if f (-x)=f (x) and odd if f (-x)=-f (x). In this article, we study even and odd functions with …

Jun 5, 2025 · In general, functions of the form f (x) = x 4, x 6, or more generally x 2 n, where the exponent is even, are examples of even functions. Another example of an even function is the …

When you plug in (-x), you get the original function back. Nothing changes. Functions containing even exponents (powers) may be even functions. For example, functions such as f (x) = x2, f …

Even and odd functions have special symmetries about the origin or y-axis. A function is even if it is symmetric about the vertical y-axis; if this is the case, f (-x) = f (x) for every x in the domain. …