Google Charts - Curved Line Chart incorrectly dips below 0

The curve may continue to dip below 0 no matter what you do, but you can crop the view so the lowest point of the displayed graph is at 0. You can do that with the vAxis.viewWindow.min property:

lineChart.draw(data, 
   {
    curveType: "function",
    vAxis: {viewWindow: {min:0} } 
   }
);

See the LineChart documentation for information on vAxis.viewWindow.min and other configuration options.

Just a quick update on this. I realised that my data work not be suitable for a curved graph anyway, as it is discrete data and not continuous. I had to switch back to straight lines, which removed my problem. Not an ideal solution, I know, but it is one that worked for me.