\(\)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 $f(x).$
+128408 If the first function has a horizontal asymptote at y =-4
Then the ratio of the coefficients on x in the numerator and denominator is a / 1 = -4
So a = -4
If it has an x itercept at (1,0)....then
-4(1) + b = 0
-4 + b = 0
b = 4
And if it has a vertical asymptote at 3.....then
3 + c =0
c = -3
So the function is
-4x + 4
f(x) = _____
x - 3
Here is a graph : https://www.desmos.com/calculator/pe4jejs6zo
