A function \( f(x) \) is considered an even function if it satisfies the following condition for all \( x \) in its domain:
\[ f(-x) = f(x) \]
This means that the value of the function at \( -x \) is equal to the value of the function at \( x \). Graphically, even functions are symmetric with respect to the y-axis.
Examples of even functions include:
- \( f(x) = x^2 \)
- \( f(x) = \cos(x) \)
- \( f(x) = x^4 \)
To determine if a specific function is even, you can replace \( x \) with \( -x \) and check if the resulting expression is equivalent to the original function. If they are the same for all \( x \) in the domain, then the function is even.