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).

haihaihai Apr 14, 2019

#1**+2 **

a) If the vertical asymptote = 3

Then this value of x makes the denominator = 0

So......3 + c = 0 ⇒ c = -3

If we have a horizontal asymptote of - 4...this implies that (ax/1x) = (a / 1) = - 4 ⇒ a = -4

And if the x intercept = then a(1) + b = 0 ...so...

-4(1) + b = 0

-4 + b = 0

b = 4

So (a, b , c ) = ( -4, 4, -3)

CPhill Apr 14, 2019