= Solution
The <domain of a function> excludes $x=3$. Both branches are positive, with a vertical <asymptote> at $x=3$ approached from both sides with value $+\infty$, and horizontal <asymptote> $y=0$ at either infinity. The graph is symmetric about $x=3$ because it depends only on $|x-3|$.
For $x<3$, the formula is $2/(3-x)$ and the <derivative> is positive; for $x>3$, it is $2/(x-3)$ and the <derivative> is negative. It passes through $(0,2/3)$ and has no zeros.
\Image[/past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2010/paper-1-reciprocal-distance.png]
{title=The two positive reciprocal-distance branches and their vertical and horizontal asymptotes}
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