Calculus AB AP test practice problem

Quote:

Originally Posted by holly123

This is a problem from the 1990 Calculus AB test.
Let f be the function that is given by f(x)= (ax+b)/(x^2-c) and that has the following properties:
i) The graph of f is symmetric with respect to the y axis
ii) lim (as x--> 2+)= +infinity
iii) f ' (1)= -2

a) determine the values of a, b, and c
b) write an eqn. for each vertical and horizontal asymptote
c) sketch the graph of f

I just need help with part a, after that i can figure out parts b and c on my own! i keep trying different things but im stuck. thank you!!

What this tells you is that $f(x)=f(-x)$

$f(-x)=\frac{-ax+b}{x^2-c}$

now we can set them equal to get

$\frac{ax+b}{x^2-c}=\frac{-ax+b}{x^2-c} \implies \frac{2ax}{x^2-c}=0$

This statement is true for all values of x so

$2ax=0 \implies a=0$

I hope this helps.

Good luck