Use the equation of the straight line to predict future deaths.

[Gamma]

Hello,

I have a set of data points to plot as graph.

X axis: Year
Y axis: Number of deaths due to cancer.

The graph is of parabolic shape opening to the right.


Following is my question:

I have been asked to plot only the first and last points and connect those points with a straight line. Use the equation of the straight line to predict future deaths.


Can this graph be considered as a function? I am not sure how to answer this. My answer is yes and No.

Yes because, by the definition of a function, you have a certain output for a certain in put. The definition does not worry about the accuracy of the output.

No because, two points in a set of data can not accurately predict the future outcomes.

Experts... what are your thoughts?


Thank You in advance.

Gamma

 

[GregA]

Hmm..seems like you're just plotting a linear function of x

This might sound a bit daft, but to answer your question another way let's say I decide that the best way to graph a cosine wave between [itex] -\pi [/itex] and [itex] \pi [/itex] is to use the following functions...
[itex] y = (\frac {2}{\pi})^2 (x+ \pi)^2 -1 [/itex] on the interval [ [itex] -\pi,\frac {-\pi}{2} ] [/itex]

[itex]y = -(\frac {2}{\pi})^2 x^2 +1 [/itex] on the interval [ [itex] \frac {-\pi}{2},\frac {\pi}{2}[/itex] ]and

[itex] y = (\frac {2}{\pi})^2 (x- \pi)^2 -1 [/itex] on the interval [[itex] \frac{\pi}{2}, \pi [/itex]]

Just because the method I employ is totally ridiculous does it make [itex] y = (\frac {2}{\pi})^2 x^2 +1 [/itex], [itex] y = (\frac {2}{\pi})^2 (x+ \pi)^2 -1 [/itex], or[itex] y = (\frac {2}{\pi})^2 (x- \pi)^2 -1 [/itex] any less functions of x?

 

[Gagle The Terrible]

A function does not have to predict accurately the future outcomes. This a problem of modeling intelligently a situation.

A funtions is roughly defined as being a relation between to variables such as for each x, there is one and only one y which is associated to.

Hence, a linear relation between to variables is a function.

A circle does is not a function because for each x, there are two values of y that are associated. You must therefore take the upper (0,Pi) OR the lower (Pi, 2Pi) part of the circle to accurately describe it as a function.

 

[Gamma]

A function does not have to predict accurately the future outcomes. This a problem of modeling intelligently a situation.

Make sense. Thank you both for your thoughts. Regards,


Gamma.

 

[daveb]

A circle does is not a function because for each x, there are two values of y that are associated. You must therefore take the upper (0,Pi) OR the lower (Pi, 2Pi) part of the circle to accurately describe it as a function.

To be correct, a circle is a function, but is a function of two variables (x and y). A function is simply a mapping from one set (call it A) to another set (call it B) such that every element of A corresponds to only 1 element of B.

 

[HallsofIvy]

No, a "circle" is not a function! It is a geometric object. What, exactly, is the function of two variables, f(x,y), that you are associating with the circle?

 

[MeJennifer]

I have a set of data points to plot as graph.

X axis: Year
Y axis: Number of deaths due to cancer.

The graph is of parabolic shape opening to the right.

Well it seems to me that if you want to extrapolate the function then clearly it is not the best approach to use a linear function that includes the first and last point of your original function.

No because, two points in a set of data can not accurately predict the future outcomes.

That depends on the function that is inter/exra-polated.
If you were to plot number of cancer deaths per 1000 people per year, the function will become a lot flatter. Then you could go one step further and plot the growth of that number per year. Then your linear extrapolation would become a bit more meaningful.