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Question

# In given problems, specify whether the given function is even, odd, or neither, and then sketch its graph.$F(x)=2 x+1$

Solution

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

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

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

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

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

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