How can you tell if a function is even or odd?

If you have a plot of the function, you can look at its symmetries. If the plot to the left of the y axis is the mirror image with respect to the y axis of the plot to the right, it's an even function. If the plot on the left is a mirror image with respect to a diagonal line going from the top left to the top right of your axes system, it is an odd function. (some example plots: f(x)=x², g(x)=cos(x), ...)If you only have the function's equation, you can try replacing x by -x and see how the function reacts. If f(-x)= f(x), f is an even function, and if f(-x)= -f(x), f is an odd function. For example, (-x)²=x² and so f(x)=x² is an even function of x.