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Question

In given problems, specify whether the given function is even, odd, or neither, and then sketch its graph.

F(x)=2x+1F(x)=2 x+1

Solution

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Answered 2 years ago
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If f(x)=f(x),xf(-x) =f(x), \quad \forall x, then the function is called an even function\textbf{even function}.

A function that gives f(x)f(x) as a sum of only even powers of xx is even.

If f(x)=f(x)xf(-x) = - f(x) \quad \forall x, then the function is called an odd function\textbf{odd function}.

A function that gives f(x)f(x) as a sum of only odd powers of xx is odd.

If f(x)f(x)f(-x) \neq f(x) and f(x)f(x)f(-x) \neq -f(x), then the function is neither even nor odd.

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