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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
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(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

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