1. ## Limit puzzle

Let f be the function that is given by f(x)=(ax+9)/(x^2-c) and that has the following properties.

a) the graph of f is symmetric with respect to the y-axis
b) lim x->2 from the right is equal to positive infinity

1) determine the values of a and c
2) write an equation for each vertical and each horizontal asymptote
3) sketch the graph
4) find the inverse

so when I started this I got the horizontal asymptote to be y=0 and the two vertical asymototes to be x=+-2 also I got the graph to be a positive hyperbola in quad 1 and the reverse of the at in quad 2 and then in between them a downwards parabola...I also think that a might be 0 but I'm not sure...any help would be great!!! Thanks

2. ## Re: Limit puzzle

When you said hyperbola and parabola, that is what those parts of the graph look like. But technically, those peices aren't hyperbolas or a parabola. It sounds like you've graphed it correctly.
Re: "I also think that a might be 0 but I'm not sure". f is never 0. (What happens when you try to solve f(x) = 0?)