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.
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Related Maths A Level answers
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