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.
🔹 Even Function
A function f(x) is even if it satisfies:
f(-x) = f(x)
Graphical meaning: Even functions are symmetric about the y-axis.
Examples:
Why? For f(x) = x²: f(-x) = (-x)² = x² = f(x)
🔹 Odd Function
A function f(x) is odd if it satisfies:
f(-x) = -f(x)
Graphical meaning: Odd functions are symmetric about the origin.
Examples:
Why? For f(x) = x³: f(-x) = (-x)³ = -x³ = -f(x)
🔹 Neither
If a function is neither even nor odd, it doesn’t have either symmetry property.
Example:
f(x) = x² + x
🔹 Summary Table
| 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 |