even--odd functions - .Foreachfunction,eitherthefunctionis...

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Four functions are depicted below. For each function, either the function is defined explicitly, or the entire graph of the function is shown. For each, decide whether it is an even function , an odd function , or neither. Background: An even function is a function whose value does not change when the sign of the input is changed. Formally, a function is an even function if for all values of in the domain of . An important feature of all even functions is that their graphs are symmetric with respect to the -axis : reflecting the graph through the -axis leaves the graph unchanged, or equivalently, the graph on the right side of the -axis is the mirror image of the graph on the left side of the -axis. The reason for this symmetry can be seen from the definition of an even function: whether we input or into the function, the function's output is the same (since ). This symmetry is illustrated in Figure 1, which shows the graph of , an even function. On the other hand, the value of an
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This note was uploaded on 02/10/2009 for the course MATH 107 taught by Professor Self during the Spring '08 term at Washington State University .

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even--odd functions - .Foreachfunction,eitherthefunctionis...

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