How do you determine even and odd functions from a graph and an equation?

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If you're trying to tell whether a function is odd or even by looking at its graph, you need to look at the end behavior.  If both ends of the graph head in the same direction (up or down), then it is an even function.  That is f(x) approaches positive infinity as x approaches both positive and negative infinity or f(x) approaches negative infinity as x approaches both positive and negative infinity.  Odd functions have ends going of in opposite directions.  If the leftmost end of the graph is approaching positive infinity, then the rightmost end has to be approaching negative infinity and vice versa.  Additionally, an even function will have either no real zeros or an even number of zeros (**zeros occur where the function crosses the y-axis).  Odd functions will have at least one or an odd number of zeros.  Also, the graph of an nth degree polynomial function will have n-1 turning points.The polynomial's degree (or largest exponent) determines if the function is odd or even.