Senior Mathematical Challenge 2016 Q9

A square has vertices at $\left(0,0\right),\left(1,0\right),\left(1,1\right)$ and $\left(0,1\right)$. Graphs of the following equations are drawn on the same set of axes as the square.

$x^2+y^2=1,$ $y=x+1$, $y=-x^2+1$, $y=x$, $y=\frac{1}{x}$

How many of the graphs pass through exactly two of the vertices of the square?