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

1. Jul 15, 2006

### 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

Last edited by a moderator: Jan 7, 2014
2. Jul 15, 2006

### 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 lets say I decide that the best way to graph a cosine wave between $-\pi$ and $\pi$ is to use the following functions...
$y = (\frac {2}{\pi})^2 (x+ \pi)^2 -1$ on the interval [ $-\pi,\frac {-\pi}{2} ]$

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

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

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

Last edited: Jul 15, 2006
3. Jul 15, 2006

### 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 wich 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.

Last edited: Jul 15, 2006
4. Jul 19, 2006

### Gamma

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

Gamma.

5. Jul 19, 2006

### daveb

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.

6. Jul 19, 2006

### HallsofIvy

Staff Emeritus
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?

7. Jul 19, 2006

### MeJennifer

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.

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.

Last edited: Jul 19, 2006