Both even and odd functions have symmetry; Just different types of symmetry. Even functions, like x^2 shown to the bottom left, have vertical symmetry, or symmetry across the Y-axis. This can be represented by the function f(-x)= f(x). Odd functions, like x^3 shown to the bottom right, have symmetry at the origin. this type of function is written f(-x)=-f(x). You can tell if a function is even by folding the graph in half. If the graph is the same on both side it is even. The same is not true for odd functions. You can create a table and if the y-coordinates are inverses of each other then it is an odd function. There isn't a family of functions that are always even or odd; although, some families are mostly even and others mostly odd. For example, squared functions are more often than not even. After this activity, I still it's a little confusing how to determine if a function is odd mathematically. Thanks for reading.
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AuthorI'm Julian Moses. this is my blog for Precalc. with Mr. Cresswell. Archives
March 2016
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