SOLUTION: A function f has horizontal asymptote of y = -4, a vertical asymptote of x = 3, and an x-intercept at (1,0). Part (a): Let f be of the form f(x) = (ax+b)/(x+c). Find an expres

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A function f has horizontal asymptote of y = -4, a vertical asymptote of x = 3, and an x-intercept at (1,0). Part (a): Let f be of the form f(x) = (ax+b)/(x+c). Find an expres      Log On


   

Question 1033903: A function f has horizontal asymptote of y = -4, a vertical asymptote of x = 3, and an x-intercept at (1,0).
Part (a): Let f be of the form
f(x) = (ax+b)/(x+c).
Find an expression for f(x).
Part (b): Let f be of the form
f(x) = (rx+s)/(2x+t).
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
I will explain just some of it.

Notice degree 1 for both numerator and denominator, equal, so that you can have horizontal asymptote. a%2F1=-4 and similarly r%2F2=-4.


The given x-intercept indicates ax%2Bb=0 and rx%2Bs=0.

You must have denominator equal to zero if x is 3, but x<>3 is the requirement for having given vertical asymptote of x=3.