Graphs of proportionality

[BornToLead]

I really need to clarify this concept so if please respond if you know the answer.

When X is directly proportional to Y the graph is a straight line passing through the origin. In case of PV=nRT, since P and n are proportional, P/n graph will look like a straight line passing through the origin.
But what kind of relationship will yield a graph like this?

Please give me examples with formulas and how to identify if the graph will be a straight line graph or the one I have attached the picture of (not exactly sure what name it has)

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[Chrisz]

I would say an exponential function would have a graph like this. F(x)=e^(-k/x). As x approaches x=0, e^(-k/x) approaches to zero. As x approches to infinity,
e(-k/x) approaches to 1. if the function is multiplied by a constant such that c(F(x))=ce^(-k/x), it would have 0 and c when x=0 and x=infinity respectively.

 

[milski]

Log(x)

The only time you will have a straight line is for a linear function, f(x)=a*x+b

The exponential function with negative power starts at 1 and decreases asymptotically to zero, which is not what is shown here.

 

[Chrisz]

Log(x)

The only time you will have a straight line is for a linear function, f(x)=a*x+b

The exponential function with negative power starts at 1 and decreases asymptotically to zero, which is not what is shown here.

Bro, look carefully at my exponential function. For ordinary e^(-kx), it would start from 1 and decreases to 0. If the exponential is e(-k/x), it will start from zero and end up at 1. So, if the function is scaled by a constant c, it will start at 0 and end up at c

 

[milski]

Bro, look carefully at my exponential function. For ordinary e^(-kx), it would start from 1 and decreases to 0. If the exponential is e(-k/x), it will start from zero and end up at 1. So, if the function is scaled by a constant c, it will start at 0 and end up at c

You're right, I did not pay attention to x being in the denominator.

On a second thought, if the problem is related to falling objects, I would say that it is most likely that we are looking at something like -ax^2 but shifted to the right, so more like -a(x-b)^2.

 

[BornToLead]

Thank you!