Not too sure if this is possible, but I have a set of data and was wondering if there was a mathematically method of calculating its vertical asymptote.
Data is from a reciprocal function, although it is "field" data so does not all strictly satisfy an equation.
x: 1.5, 2, 3, 4, 5, 6, 7, 8, 10, 15
y: 56, 20, 10.2, 7.6, 6, 5, 4.3, 3.8, 3.1, 2.5
The horizontal asymptote is at y = 1
"Using what you have discovered about the function y=(A/(x+B))+C, find a reciprocal function that could be used as a model for this data. Fully justify all decisions regarding the values of A, B and C based on your knowledge of transformations"
I don't believe there is enough information to calculate the function of the above data. If I had the vertical asymptote, I would be able to use a pair of coordinates and the two asymptotes to find A. Right?
Even so, since the data is "field data", isnt the only way to "determine" a function by using hyperbolic regression (line of best fit)?
Is there an algebraic method to determine the vertical asymptote?
If not, can I simply use (as the question asks) transformations of A and C to determine B?
More likely, how would I be able (as accurately as possible) use hyperbolic or linear regression to determine the vertical asymptote? (Help with this would be much appreciated, regression scares me :S)
Thanks in advance. I know this question is long and a little messy but its really holding me back from finishing my work.