3. Determine whether the function f(x)= is even, odd, or neither. Explain your reasoning.

## Step 1: Evaluate $f(-x)$<br />### We substitute $-x$ for $x$ in the function $f(x)$ and simplify. $f(-x) = (-x)^3 + 2(-x) = -x^3 - 2x$<br /><br />## Step 2: Compare $f(-x)$ with $f(x)$ and $-f(x)$<br />### We compare the expression for $f(-x)$ obtained in the previous step with the original function $f(x) = x^3 + 2x$ and its negative, $-f(x) = -(x^3 + 2x) = -x^3 - 2x$. We observe that $f(-x) = -x^3 - 2x$, which is equal to $-f(x)$.<br /><br />## Step 3: Determine the function's symmetry<br />### Since $f(-x) = -f(x)$, the function $f(x)$ is an odd function. This indicates symmetry about the origin.