A function f has a horizontal asymptote of y = -4, a vertical asymptote of x = 3, and a x-intercept at (1, 0).

Part A: Let f be of the form f(x) = (ax + b)/(x + c). Find an expression for f(x).

Part B: Let f be of the form f(x) = (rx + 3)/(2x + t). Find an expression for f(x).

Guest Sep 19, 2019

#1**+1 **

__Part A__

The degree of the numerator is equal to the degree of the denominator, so the horizontal asymptote is

y = a / 1 which we know is -4

a / 1 = -4

a = -4

There is a vertical asymptote at x = 3

So we know when x = 3 , x + c = 0

3 + c = 0

c = -3

Now we know: f(x) = (-4x + b)/(x - 3)

There is an x-intercept at (1, 0) so we know

f(1) = 0

(-4(1) + b)/(1 - 3) = 0

(-4 + b)/( -2 ) = 0

-4 + b = 0

b = 4

Altogether: f(x) = (-4x + 4)/(x - 3)

hectictar Sep 19, 2019