`g(x) = cot(x)` Use the graph of the function to determine whether the function is even, odd, or neither. Verify your answer algebraically.

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The graph of g(x)=cot(x) is shown below.

We know that sin(-x)=-sin(x) and cos(-x)=cos(x).

So, `cot(-x)=\frac{cos(-x)}{sin(-x)}=\frac{cos(x)}{-sin(x)}=-cot(x)`

Hence, cot (x) is an odd function, and its graph is symmetric with respect to the origin.

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The graph of g(x)=cot(x) is shown below.

We know that sin(-x)=-sin(x) and cos(-x)=cos(x).

So, `cot(-x)=\frac{cos(-x)}{sin(-x)}=\frac{cos(x)}{-sin(x)}=-cot(x)`

Hence, cot (x) is an odd function, and its graph is symmetric with respect to the origin.

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