Question

Even functions and odd functions are often mistaken as being defined as such because of their exponents. While this comes into play, what exactly makes a function even or odd?

Answer 1

Even functions are symmetric about the y-axis, while odd functions are symmetric about the origin.

Step-by-step explanation:

An even function is a function that satisfies the property y(x) = y(-x), while an odd function is a function that satisfies the property y(x) = -y(-x). The key difference between even and odd functions lies in their symmetry.

An even function is symmetric about the y-axis, which means that if you reflect the function about the y-axis, it remains unchanged. On the other hand, an odd function is symmetric about the origin, which means that if you reflect the function about the origin, it remains unchanged.

For example, the function f(x) = x^2 is even because f(x) = f(-x), while the function g(x) = x^3 is odd because g(x) = -g(-x).