# Determine Equation by Graph

1. Dec 9, 2004

### aisha

OK I am given the graph of a reciprocal function the asymptotes are x=1 and x=-1
3 | 4

Ok in the first quadrant there is a > looking curve going through the invariant point 1 and in the second quadrant there is a < curve going through the invariant point 1. then there is a parabola with a max of -1 inbetween the asymptotes.

The question says determine the equation of the graph, so I need to find f(x) and then to get the reciprocal just put 1/(f(X)). I sketched f(x) but how do I find out the eqn?

2. Dec 9, 2004

### Galileo

Does it look like the $$f(x)=\frac{1}{4*x^2-1}$$ in your other thread?

If so, try a function with a similar form: $$f(x)=\frac{a}{bx^2-c}$$
and find a,b and c by plugging in coordinates from the graph.

3. Dec 11, 2004

### aisha

no i graphed the equation in my other post it does not look similar to this one. I still have no idea of how to determine the equation, all I know is to find the equation of f(x) first then find 1/f(x).

Well this is what I just tried since the vertex of f(x) is 0,-1 I subbed this into the equations y=a(x+h)^2-K and then I took a point from the graph (the invariant point, 1,1) and then solved for a... a=2 so my equation for f(x) became 2x^(2)-1 that means the reciprocal must be 1/2x^(2)-1
Im not sure if this is the correct way, I tried graphing the equation using my ti 83 graphing calculator, but the reciprocal function looks different from the one on my hand out, so i cant check If I am right? What do I do? does this seem right? please HELP ME !!!

Last edited: Dec 11, 2004
4. Dec 14, 2004