Build functions

[adan]

Hi,
This is part of a project I am currently working on. I want to build two functions of one indpenendent variable x between 0-1, and the dependent variable y between 0-5. In the first function y and x have a positive relation. In the second function, y has a negative relation with x.

Any suggestion?

Best Regards

 

[Steven G]

Did you think of drawing a line from the y axis at 5 to the x-axis at 1? That will be the negative function. Can you figure out how to get the positive function?

 

[adan]

Did you think of drawing a line from the y axis at 5 to the x-axis at 1? That will be the negative function. Can you figure out how to get the positive function?

Thanks @Jomo. The negative function can be an inverse [MATH]5/(1+x)[/MATH], the positive can be [MATH]5x[/MATH], but most values of x are larger than 0.5 with few values less than 0.5, and the likelihood of getting y larger or equal to 3 should be large.

 

[Steven G]

Draw a line from the origin to the point (1,5).
What is the equation of this line? What is the equation of the line that I gave you in my earlier post?
Do these lines satisfy your conditions?

 

[Dr.Peterson]

Hi,
This is part of a project I am currently working on. I want to build two functions of one independent variable x between 0-1, and the dependent variable y between 0-5. In the first function y and x have a positive relation. In the second function, y has a negative relation with x.

Any suggestion?

Best Regards

Perhaps you need to define for us what you mean by "positive relation" and "negative relation", in case we have a different idea in mind.

 

[adan]

Perhaps you need to define for us what you mean by "positive relation" and "negative relation", in case we have a different idea in mind.

Positive means the dependent variable increases/decreases when the independent increase/decrease and the negative is the opposite.

 

[Otis]

Positive means the dependent variable increases/decreases when the independent increase/decrease and the negative is the opposite.

Hi adan. What you're describing above, I learned as 'direct variation' and 'inverse variation'.

For your "negative relation" (inverse variation), does the following match what you're thinking about?

\(\displaystyle g(x) = \frac{(25 - 15\sqrt{5})x - 25 + 15\sqrt{5}}{10x - 5 + 3\sqrt{5}}\\

g(0) = 5\\

g(1) = 0\)


?

 

[Dr.Peterson]

Positive means the dependent variable increases/decreases when the independent increase/decrease and the negative is the opposite.

By this definition, what Jomo has suggested is appropriate: a line with positive slope, and a line with negative slope.

On the other hand, people often misunderstand definitions in this area. If what you really mean is what I call direct and inverse variation, the former is not just any increasing function, but a linear function passing through (0, 0), and the latter is not just any decreasing function, but a reciprocal function.

But from what you said in post #3, it appears that you have additional requirements that you haven't stated, which presumably arise from the nature of your unstated project. Please give us additional background.