The technical definition of an Even Function is one that adheres to the following rule:

$$f(-x)=f(x)$$

But what exactly does this mean? It means that even if we make an input negative, the output will be the same. For example, if we input the number $3$ into a certain function and then input the number $-3$, the output will be the same in both cases.

The less technical definition of an even function is one in which the exponents are either even numbers or $0$. The $0$ exponent is for constants.

For example, if $f(x)$ equals $x^2$ or $x^6 + x^4$ or $x^{10} + 7$, it'd be an even function.

The technical definition of an Odd Function is one that adheres to the following rule:

$$f(-x)=-f(x)$$

But what exactly does this mean? It means that when we make the input negative, the output will be the same value but now the opposite sign. For example, if we input the number $3$ into a certain function and the output is $10$, and then we input the number $-3$ into the same function, the output will be $-10$.

The less technical definition of an odd function is one in which the exponents are odd integers.

For example, if $f(x)$ equals $x$ or $x^3 + x$ or $x^9 + x^7 + x^3$, it'd be an odd function.