Here are the essential concepts you must grasp in order to answer the question correctly.
Even Functions
A function is classified as even if it satisfies the condition f(-x) = f(x) for all x in its domain. This means that the graph of the function is symmetric with respect to the y-axis. For example, the function f(x) = x^2 is even because f(-x) = (-x)^2 = x^2.
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Odd Functions
A function is considered odd if it meets the condition f(-x) = -f(x) for all x in its domain. This indicates that the graph of the function is symmetric with respect to the origin. An example of an odd function is f(x) = x^3, as f(-x) = (-x)^3 = -x^3.
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Neither Even Nor Odd Functions
A function is classified as neither even nor odd if it does not satisfy the conditions for either classification. This means that the function does not exhibit symmetry about the y-axis or the origin. For instance, the function f(x) = x + 1 is neither even nor odd, as f(-x) = -x + 1 does not equal f(x) or -f(x).
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