A function f has a 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 \(f(x) = \frac{ax+b}{x+c}\).Find an expression for f(x). Part (b): Let f be of the form \(f(x) = \frac{rx+s}{2x+t}\) .Find an expression for f(x). a,b,c,r,s,t are just variables

MIRB16
Aug 28, 2017

#1**+1 **

(a) If the horizontal asymptote is -4, then a = -4

If the vertical asymptote is 3, then c = -3

And if the x intercept is (1,0), then -4 (1) + b = 0 ......so b = 4

Here is the graph : https://www.desmos.com/calculator/5rlx6oppr0

(b) If the horizontal asymptote is -4, then r = -8

If the vertical asymptote is 3.....then 2(3) + t = 0 → t = -6

And if the x intercept is (1,0), then -8(1) + s = 0 → s = 8

Here is the graph : https://www.desmos.com/calculator/k3gd6mxdun

CPhill
Aug 28, 2017