SOLUTION: 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) = {ax+b}/{x+c}. Find an expressio

Algebra ->  Rational-functions -> SOLUTION: 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) = {ax+b}/{x+c}. Find an expressio      Log On


   

Question 1063757: 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) = {ax+b}/{x+c}. Find an expression for f(x). Part (b): Let f be of the form f(x) = {rx+s}/{2x+t}. Find an expression for f(x).
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
This will be part (a) only.

Horizontal asymptote, y=-4
Vertical Asymptote, x=3
x-intercept, (1,0)
Form of function f%28x%29=%28ax%2Bb%29%2F%28x%2Bc%29

For unbounded x, f gets closer to -4=ax%2Fx, or highlight%28a=-4%29.

f will be undefined and here makes a vertical asymptote, if x%2Bc=x-3, or highlight%28c=-3%29.

The zero at x=1 means ax%2Bb=0
b%2Bax=0
b=-ax
b=-%28-4%29%2A1
highlight%28b=4%29

Make the substitutions for your function.