"y as a function of x" meaning (2024)

sp3sp2sp said:

If you are told to plot something as a function of something else, such as "pressure as a function of volume" would volume always go along x-axis? I mean what does it matter if you put volume on y-axis ,and then put pressure on x-axis? thanks

You could put pressure on the p-axis and volume on the v-axis.

sp3sp2sp said:

If you are told to plot something as a function of something else, such as "pressure as a function of volume" would volume always go along x-axis? I mean what does it matter if you put volume on y-axis ,and then put pressure on x-axis? thanks

It's only a convention to put the variable on the ##x-##axis and the value on the ##y-##axis, as e.g. also in bar charts. There are all kind of diagrams out there: non-linear scaling, two value axis for different quantities or what so ever. It is all about readability, and it avoids a lot of confusion and unnecessary discussions to follow conventions.

sp3sp2sp said:

OK thanks but so when professor asks for this as a function of that, I should be thinking plot this on x and that on y, right? (because for one reason its convention)?

Usually, yes. It's faster to read. However, there might be circ*mstances, where it is different: form of paper, resp. printer, multiple values, the need to mirror the function along the diagonal etc. But usually we have as a function ##f(x)=y(x)=y\,.##

"when professor asks for this as a function of that, I should be thinking plot this on x and that on y, right? (because for one reason its convention)?"

no, just the opposite is the usual convention. i.e. here "this" = y and "that" = x.

mathwonk said:

no, just the opposite is the usual convention. i.e. here "this" = y and "that" = x.

yup that's actually what i meant..i just reread and just got them mixed up..thank you.

I have plotted moment of inertia as a function of radius using 4 data points and I am asked if this graph is linear but the plot is is not smooth at all even though it definitely has positive slope. Then I am asked what I could do to make the plot linear and wouldn't this just be getting the equation? Its y = (1.374e-2)x - 5.706e-4

thanks for any more help

sp3sp2sp said:

If you are told to plot something as a function of something else, such as "pressure as a function of volume" would volume always go along x-axis? I mean what does it matter if you put volume on y-axis ,and then put pressure on x-axis? thanks

First answer, yes. The vertical axis is coordinates for the function and dependent variable, and horizontal axis is for coordinates for the independent variable. The FUNCTION has inputs of your volume values.

Do you expect an exponential function?

It is not linear, sure, but not everything nonlinear is exponential.

sp3sp2sp said:

I have plotted moment of inertia as a function of radius using 4 data points and I am asked if this graph is linear but the plot is is not smooth at all even though it definitely has positive slope. Then I am asked what I could do to make the plot linear and wouldn't this just be getting the equation? Its y = (1.374e-2)x - 5.706e-4

That

a linear equation, but where did it come from? If the four data points you mentioned in post 10 lie on a curve, then the above could not possibly be the equation of the graph the data points lie on.

sp3sp2sp said:

I have graphed inertia as function of radius

Inertia and radius of what? It would help a lot if you tell us some details of the experiment or situation that you are trying to analyze.

[added] OK, now I've seen your other current thread. Are you discussing the same situation as in that thread, and by "inertia" do you mean "moment of inertia"?

If the two threads are about the same situation, we'll merge them together for you.

sp3sp2sp said:

I have plotted moment of inertia as a function of radius using 4 data points and I am asked if this graph is linear but the plot is is not smooth at all even though it definitely has positive slope. Then I am asked what I could do to make the plot linear and wouldn't this just be getting the equation? Its y = (1.374e-2)x - 5.706e-4

thanks for any more help

I no longer know much from Physics or Mechanics, but if you have original data which would fit a curve for an exponential function, you could treat your data or your model equation so that it would work as a linear function. One set of coordinates might go onto semilog number scale and the other set of corresponding coordinates could go on to a linear number scale and if you have something that looks like a line, then you could form the necessary equation. Other members can explain this better and show it.

sp3sp2sp said:

After I make it linear the slope should = the mass shouldn't it? It looks exponential, I mean I am not sure what else to call it. It intercepts at origin and increases with curved pos slope. thanks for the help

You can run a regresion analysis and try to deetmine the best fit through it. Linarity is given in terms of the coefficients, not the variables. If you have differentiability you may use the inverse / implicit function theorems.

I'm not a mathematician, but my old maths teacher told me that log-log works for most equations I'll meet.
If you expect it to be x, x^2, x^3 , 1/x , √x , etc. then it will tell you which.
This is just some made up data:

BTW the lines were sketched by Excel just for speed and convenience. I don't like that and would get a better line by hand, when I know what answer I want ! Only joking, but humans really can do better, because we know the 0,0 must be on the line even though we can't collect that data.

Merlin3189 said:

I'm not a mathematician, but my old maths teacher told me that log-log works for most equations I'll meet.
If you expect it to be x, x^2, x^3 , 1/x , √x , etc. then it will tell you which.
This is just some made up data:
View attachment 235572
BTW the lines were sketched by Excel just for speed and convenience. I don't like that and would get a better line by hand, when I know what answer I want ! Only joking, but humans really can do better, because we know the 0,0 must be on the line even though we can't collect that data.

But (0,0) does not seem to be on your graph. For "standard" regression we have that ( x-bar, y-bar) are in the least squares line of best fit.

Merlin3189 said:

Only joking, but humans really can do better, because we know the 0,0 must be on the line even though we can't collect that data.

You can force the fit to go through that line.
Not all lines have to go through 0,0.

WWGD said:

But (0,0) does not seem to be on your graph.

I don't know how to measure that data point: zero radius is impracticable.
I should have simply selected the option in Excel to force the line through 0,0 as suggested by MFB. I only thought about that when I noticed Excel had done it wrong and I forgot that it has such an option.

mfb said:

You can force the fit to go through that line.
Not all lines have to go through 0,0.

But this line does. Even if you don't yet know the form of the function for moment of inertia, you do know that if an object had all its mass concentrated at zero radius, it would have zero moment of inertia.

It is very traditional to use the horizontal axis as the independent variable and the vertical axis as the dependent variable. You can and should perform translations (like log(y)) if it makes the graph easier to use and to read the numbers of interest from. Just be sure that the axis is labeled correctly "log(pressure)" and that the numbers reflect that (values of log(pressure) rather than of pressure). Alternatively, you can position the dependent values in their log(pressure) position, but label that axis as pressure and put the pressure numerical values at that axis position.

Although using the variables "x" and "y" to describe a graph is very common, you should get in the habit of using the correct variable (like "pressure" and "volume") when you talk about a specific graph and use "horizontal axis" rather than "x axis" and "vertical axis" rather than "y axis" when describing the layout of a general graph.