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## 'Curve Match' printed from http://nrich.maths.org/

The following five functions have been plotted accurately on the
chart below

$$y=\sqrt{x}\quad\quad y=x^2\quad\quad y=x\quad\quad
y=(x^2+x)/2\quad\quad y=2\sqrt{x}-x$$

Which is the $x$-axis and which is the $y$-axis? Which curves
correspond to which functions?

Imagine that you wish to plot a route between $(0, 0)$ and $(1,
1)$. Can you find a function which does this without intersecting
any of the existing curves, except at the endpoints?

What other curves can you plot which only intersect the existing
curves at the end points?