I started with plotting this equation of a convex hyperbola:
y = 2/x
Which of course looks like this (I'm only interested in 1st quadrant):
Now, I want to plot the same function, but have it flipped about, such that it becomes concave. What is the formula for that? It should look concave, like this:
y = ???
Note: I made these graphs myself, don't scrutinize them too much!
$y=\frac{2}{x}$ is its own reflection across the line $y=-x$ (it is already 'concave' for $x\leq0$). You only need to shift the viewing window to the lower-left quadrant or translate the function right and up by some suitable distance.
The curve $y-a=f(x-b)$ is the translation of the curve $y=f(x)$ upwards by $a$ and to the right by $b$. This is why GNUSupporter8964民主女神地下教會 commented $y=k+\frac{1}{x-c}$. If you want to shift the graph upwards by $k$ and to the right by $c$, you would solve for $y$ in the equation $y-k=f(x-c)$ where $f(x)=your\ function=\frac{2}{x}$.
$$f(x)=\frac{2}{x};\quad y=f(x);\quad y-k=f(x-c)\implies y=\frac{2}{x-c}+k$$