= Solution
At a true <variance> $\sigma^2>0$, $S/\sigma^2\sim\chi_n^2$. Therefore the <power function> is
$$
\boxed{w(\sigma^2)=1-F_n\left(\frac{\sigma_0^2}{\sigma^2}F_n^{-1}(1-\alpha)\right).}
$$
The argument of $F_n$ decreases as $\sigma^2$ increases. Since the chi-squared density is positive on the positive half-line, the power is continuous and strictly increasing, with
$$
\boxed{w(0^+)=0,\qquad w(\sigma_0^2)=\alpha,\qquad w(\infty)=1.}
$$
These features determine the requested rough sketch. The curve passes through the size at the null value and approaches one for very large <variance>.
\Image[/past-exam-of-the-options-ii-course-of-the-university-of-oxford/2013-variance-test-power.png]
{title=Power rises from zero through the test size to one as the <variance> increases}
{description=Original illustrative power curve for n=4 and alpha=0.05, plotted against the ratio of the true <variance> to the null <variance>. The marked point has ratio one and power alpha.}
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