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Math Help - Calculus AB AP test practice problem

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    Calculus AB AP test practice problem

    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!!
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    Quote Originally Posted by holly123 View Post
    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
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