If the range of the real valued function $f(x) = \frac{x^2 + x + k}{x^2 - x + k}$ is $[\frac{1}{3}, 3]$, then $k =$
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For a rational function $y = \frac{ax^2+bx+c}{dx^2+ex+f}$, to find the range, rearrange it into a quadratic equation in $x$. Then, use the condition that the discriminant ($\Delta$) must be non-negative ($\Delta \geq 0$) since $x$ is real. The resulting inequality in $y$ will give the range. The boundary values of the range are the roots of the equation $\Delta = 0$.