+752 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
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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
