You can tell if a function is even or odd by looking at its graph and how it shows symmetry:

Even Functions

• What It Means: A function called $f(x)$ is even if changing the sign of $x$ doesn’t change the value of the function. In simpler terms, $f(-x) = f(x)$ for every $x$.
• Symmetry: The graphs of even functions look the same on both sides of the y-axis (the vertical line in the middle).
• Example: A good example is the graph of $f(x) = x^2$. It is symmetrical around the y-axis.

Odd Functions

• What It Means: A function $f(x)$ is odd if changing the sign of $x$ flips the sign of the function’s value. So, we have $f(-x) = -f(x)$ for all $x$.
• Symmetry: The graphs of odd functions have a symmetry around the origin (the point where the x and y axes cross).
• Example: The graph of $f(x) = x^3$ shows this kind of symmetry.

By looking at these features, you can quickly tell whether a function is even or odd!