Consider the function: f(x) = (x+a)/(bx+2)

The curve crosses the point P (0,1/2)

And the line (y=1) is an asymptote.

Find a and b... Help is very much appreciated !!! thank you!!

Printable View

- January 21st 2010, 01:46 AMYehiaA function, find "a" and "b" ?
Consider the function: f(x) = (x+a)/(bx+2)

The curve crosses the point P (0,1/2)

And the line (y=1) is an asymptote.

Find a and b... Help is very much appreciated !!! thank you!! - January 21st 2010, 02:40 AMpakomo
You might not know this, but:

If the degree of the numerator (x+a) and the deniminator (bx+2) are equal, then the asymptote is equal to the ratio of the leading coefficients of the two.

Ask yourself: What is the asymptote's level? It is y=1. Now ask, what are the leading coefficients of x+a and bx+2? How can you express 1 as a ratio of the two coefficients?

This should answer your need to find b.

Now ask yourself: What can I use the other information ( (0,f(0)) = (0,1/2) ) for? Well, you can find a. Try inserting 0 in your function. What do you get? How can you find a from this new information, and the fact that f(0)=1/2?

You should be done by now :)

Happy mathing