7.79 The graph of the inverse proportion function $y=\frac{k}{x}$ (where $x$ is the independent variable, and $k$ is a non-zero and non-1 constant) is an axisymmetric figure. Its axis of symmetry is which of the following linear functions?
(A) $y=\frac{-k}{|k|} x$.
(B) $y=|k| x$.
(C) $y=-k x$.
(D) $y=k x$.
(China Guangzhou, Wuhan, Fuzhou, and other five cities junior high school mathematics league, 1988)
[Solution] $\because y=\frac{k}{x}$ has two axes of symmetry: $y= \pm x$.
Also, $\because \quad y=\frac{-k}{|k|} x= \pm x$, therefore the answer is $(A)$.