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If we want to make a graph then can the staring points for x-axis and y-axis be different? For example; if the starting point of x-axis is 0 then can it be 10 for y-axis?

In the following graph, concentration and density are plotted. The starting point for x-axis is 0 while for y-axis it is 2. What does it mean? Does it mean that when concentration is 0, density is 0.95? It is impossible.

enter image description here

Rafique
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    Your words don't match the labels on the graph. You say 0.95 but the graph says 2. – dfeuer Dec 15 '13 at 05:05
  • sorry, it is 2 now. – Rafique Dec 15 '13 at 05:06
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    The intervals over which you choose to graph a function are entirely up to you. Similarly, you can choose arbitrary scaling as well. – abiessu Dec 15 '13 at 05:07
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    It's just a way of focusing on the important information. – Alec Dec 15 '13 at 05:08
  • i had uploaded the wrong graph. Sorry for that. – Rafique Dec 15 '13 at 05:12
  • To be clear, the y-axis is measuring the density of sodium chlorate? I think your question is more of a chemistry problem than a math one. I would guess that whoever made the graph extended their curve to x=0 by extrapolating from their given data (though it seems odd that they didn't have it pass through the origin). – andraiamatrix Dec 15 '13 at 05:25
  • It's just notation. Axis are drawn simply to orient the reader so that they know what is what. They can be put whereever you like. – Stephen Montgomery-Smith Dec 15 '13 at 05:36
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    @andraiamatrix: The density of pure water is close to $1$ g/ml at $4$ C, so the curve should not go through $(0,0)$ – Ross Millikan Dec 15 '13 at 05:38
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    It is important that the plot area be restricted to the area of interest. Just for fun, plot y = 1000 + Sin(x) for 0 < x < 100 but start the y axis at zero; you will almost see an horizontal line. Be always cautious when you look at a plot (in particular on TV or newspaper). Depending on the message to be delivered, the same numbers could appear extremely different. – Claude Leibovici Dec 15 '13 at 05:45

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You can imagine the graph going over the whole real plane. The paper isn't large enough to show that, so we print the part of the graph that is of interest. In this case, we could extend the plot downward so we could show Density of zero. It looks like none of the curves would go through the new area, so (given the area of the printed page or window onscreen) no new information would be portrayed. Then we would have to shrink the part that is currently shown, so it would be harder to read values off the graph.

In this case, it doesn't make sense to extend the $x$ axis beyond $0\%$ to $100\%$, but the point is the same-display the region of interest. This tends to accentuate variation. In this case, it looks like the density increases a lot with concentration, but really it only increases in proportion to the concentration. That shows that the reader has to pay attention.

Ross Millikan
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