After a while spent as a toughnut, we recieved the solution to this problem. We were very pleased to see that one of our younger solvers, Jonathan, realised that the first graph was $y=0.5 x$. Impressively, a full solution was sent in by James from Bay House, where all of his functions gave a close fit with the data -- well done James!

James' suggestions agreed with ours in six of the cases (bold font), but differed in four cases (normal font). Perhaps you might like to consider which you feel are the closer fit?

Experiment 1: $y=x/2$

Experiment 2: $y=\sin(x) $

Experiment 3: $y=x^2$

Experiment 4: $y=x-\sin(2x)$

Experiment 5: $y=5\log_{45}(x+1)$ $\left(\mbox{we got }y=\sqrt{x}\right)$

Experiment 6: $y=(\sin(1.7x)+1)/2$ $\left(\mbox{we got }y=\sin^2(x)\right)$

Experiment 7: $y=-0.6+(\log_{10}(6x))^{-1}$ $\left(\mbox{we got }y=\frac{1}{1+x^2}\right)$

Experiment 8: $y=\log_{15}(7x+1)$ $\left(\mbox{we got }y=1.65x/(1+x)\right)$

Experiment

Experiment