A function is said to be even if it satisfies the condition f(x) = f(-x) for all values of x in its domain. In other words, if you reflect the graph of an even function across the y-axis, you will get the same graph.
For example, the function f(x) = x^2 is an even function since f(x) = f(-x) for all values of x:
f(x) = x^2 f(-x) = (-x)^2 = x^2
On the other hand, a function is said to be odd if it satisfies the condition f(x) = -f(-x) for all values of x in its domain. In other words, if you reflect the graph of an odd function across the origin, you will get the same graph.
For example, the function f(x) = x^3 is an odd function since f(x) = -f(-x) for all values of x:
f(x) = x^3 f(-x) = (-x)^3 = -x^3 -f(-x) = -(-x)^3 = x^3
To determine whether a function is even or odd, you can check whether the function satisfies the conditions mentioned above. If f(x) = f(-x), the function is even, and if f(x) = -f(-x), the function is odd. If neither condition is satisfied, the function is neither even nor odd.