- Forums
- Mathematics
- General Math

- B
- Thread startersp3sp2sp
- Start date
- Tags
- Function

In summary, the conversation discusses the convention of plotting variables on the x-axis and values on the y-axis, the possibility of making a curved line graph linear, and the process of linearization. It also includes a question about a specific equation and its relation to the plotted data points.

- #1

sp3sp2sp

- 100

- 4

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

Mathematics news on Phys.org

- #2

PeroK

Science Advisor

Homework Helper

Insights Author

Gold Member

2023 Award

- 27,432

- 18,903

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.

- #3

fresh_42

Mentor

Insights Author

2023 Award

- 19,385

- 25,231

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.

- #4

sp3sp2sp

- 100

- 4

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)?

- #5

fresh_42

Mentor

Insights Author

2023 Award

- 19,385

- 25,231

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\,.##

- #6

mathwonk

Science Advisor

Homework Helper

- 11,732

- 1,996

"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.

- #7

sp3sp2sp

- 100

- 4

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.

Last edited by a moderator:

- #8

sp3sp2sp

- 100

- 4

Is it possible to make a curved line graph linear? I tried squaring x-values , but doesn't that mean I would have to also square y-values = exact same graph? thanks

- #9

mfb

Mentor

Insights Author

- 37,183

- 14,027

You can rescale axes - sometimes this makes relations easier to see, sometimes it doesn't. It depends on your function. As an example, ##f(x)=e^x## is a straight line if you make the y-axis logarithmic.

- #10

sp3sp2sp

- 100

- 4

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

- #11

symbolipoint

Homework Helper

Education Advisor

Gold Member

- 7,358

- 1,835

sp3sp2sp said:

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.

- #12

sp3sp2sp

- 100

- 4

I have graphed inertia as function of radius and the curve looks exponential. I want to linearize the curve. If I take log of all the y-values would that work and does that make math sense to do that? thanks for any help

- #13

lekh2003

Gold Member

- 536

- 340

Yes you could do that, I have seen it been used a few times in some Physics Olympiad questions. However, *why* you want to do it is up to you.

- #14

mfb

Mentor

Insights Author

- 37,183

- 14,027

Do you expect an exponential function?

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

- #15

Mark44

Mentor

Insights Author

- 37,702

- 10,008

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

__is__

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.

- #16

sp3sp2sp

- 100

- 4

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

- #17

jtbell

Staff Emeritus

Science Advisor

Homework Helper

- 15,951

- 5,976

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.

Last edited:

- #18

symbolipoint

Homework Helper

Education Advisor

Gold Member

- 7,358

- 1,835

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.

- #19

fresh_42

Mentor

Insights Author

2023 Award

- 19,385

- 25,231

I have merged the two threads, as I suspected we were still talking about the function in your post #10. If so, the answers you will get to your post #12 will be misguiding. If I'm wrong, then just mention what exactly you have plotted.

- #20

sp3sp2sp

- 100

- 4

its OK its a lab that's already completed. It was time sensitive question that's why I thought I would ask the exact issue I was having but it turns out I just needed to square the R value to linearize the plot. (because I = .5MR^2).. That was the problem i was having: How to linearize moment of inertia vs radius plot Thank you for all the help.

- #21

WWGD

Science Advisor

Gold Member

- 7,169

- 10,827

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.

- #22

Merlin3189

Homework Helper

Gold Member

- 1,730

- 818

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.

#### Attachments

- #23

WWGD

Science Advisor

Gold Member

- 7,169

- 10,827

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.

- #24

mfb

Mentor

Insights Author

- 37,183

- 14,027

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.

- #25

Merlin3189

Homework Helper

Gold Member

- 1,730

- 818

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.

- #26

FactChecker

Science Advisor

Homework Helper

Gold Member

2023 Award

- 8,724

- 4,191

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.

Last edited:

## Related to "y as a function of x" meaning

## 1. What does "y as a function of x" mean?

"Y as a function of x" is a mathematical expression that represents the relationship between two variables, y and x. It means that the value of y is dependent on the value of x and can be expressed as a function of x. In other words, the value of y changes according to the value of x, and this relationship can be described using mathematical equations.

## 2. How is "y as a function of x" different from "x as a function of y"?

The difference lies in which variable is considered the independent variable and which is the dependent variable. In "y as a function of x", x is the independent variable and y is the dependent variable. This means that the value of y is determined by the value of x. In "x as a function of y", y is the independent variable and x is the dependent variable. This means that the value of x is determined by the value of y.

## 3. What is the purpose of expressing a relationship as "y as a function of x"?

Expressing a relationship as "y as a function of x" allows us to understand and analyze the relationship between two variables. It helps us to make predictions and understand how changes in the value of x affect the value of y. It is also a fundamental concept in mathematics and is used in various fields such as physics, economics, and engineering.

## 4. Can "y as a function of x" be a linear relationship?

Yes, "y as a function of x" can represent a linear relationship. In a linear relationship, the change in y is directly proportional to the change in x. This can be represented by a straight line on a graph, with the slope of the line indicating the relationship between y and x.

## 5. How can "y as a function of x" be used in real-world applications?

"Y as a function of x" can be applied in various real-world situations, such as predicting the growth of a population, determining the relationship between price and demand in economics, and modeling the trajectory of a projectile in physics. It is a powerful tool for understanding and analyzing relationships between variables and making informed decisions based on this understanding.

### Similar threads

BInverse Functions: Why rewrite as y=f(x) ?

- General Math

- Replies
- 11

- Views
- 879

IHow can Euler angles be visualized using a polar plot?

- General Math

- Replies
- 1

- Views
- 1K

IVolume of Solid of Revolution (About the line y = x)

- General Math

- Replies
- 6

- Views
- 1K

IWhat are the applications of inverses of vector functions?

- General Math

- Replies
- 17

- Views
- 2K

ICreating a function with specific shape, intercepts, integral....

- General Math

- Replies
- 1

- Views
- 927

ICan Angular Velocity Accurately Control Ragdoll Limbs in Game Physics?

- General Math

- Replies
- 5

- Views
- 1K

BHow to find the infinitesimal coordinate transform along a hyperbola?

- General Math

- Replies
- 1

- Views
- 905

BQuestion about Notation of Function

- General Math

- Replies
- 12

- Views
- 1K

Exploring an Unexplored Expression for the Beta Function

- General Math

- Replies
- 2

- Views
- 1K

IWhich kind of function is this?

- General Math

- Replies
- 3

- Views
- 805

- Forums
- Mathematics
- General Math