An online even or odd function calculator will help you to identify a certain function is even, odd, or neither function. Usually, the sign of values in the function did not matter during the calculation of function values, and only half values in the domain will be used. In this article, we will look at the definitions, properties, and how to find if a function is even or odd.
A function f(x) is even if it satisfies:
f(-x) = f(x)
Graphical meaning: Even functions are symmetric about the y-axis.
f(x) = x²f(x) = |x|f(x) = cos(x)Why? For f(x) = x²: f(-x) = (-x)² = x² = f(x)
A function f(x) is odd if it satisfies:
f(-x) = -f(x)
Graphical meaning: Odd functions are symmetric about the origin.
f(x) = x³f(x) = sin(x)f(x) = xWhy? For f(x) = x³: f(-x) = (-x)³ = -x³ = -f(x)
If a function is neither even nor odd, it doesn’t have either symmetry property.
f(x) = x² + x
f(-x) = (-x)² + (-x) = x² - xf(-x) ≠f(x) and f(-x) ≠-f(x)| Type | Condition | Symmetry | Examples |
|---|---|---|---|
| Even | f(-x) = f(x) |
y-axis | x², cos(x), |x| |
| Odd | f(-x) = -f(x) |
Origin | x³, sin(x), x |
| Neither | Neither condition holds | No symmetry | x² + x, eˣ |