SOLUTION: Write an equation for a rational function with the given characteristics: Vertical asymptotes at x = −3 and x = 6, x-intercepts at (−4, 0) and (1, 0),horizontal asym

Algebra ->  Rational-functions -> SOLUTION: Write an equation for a rational function with the given characteristics: Vertical asymptotes at x = −3 and x = 6, x-intercepts at (−4, 0) and (1, 0),horizontal asym      Log On


   

Question 1128113: Write an equation for a rational function with the given characteristics:
Vertical asymptotes at x = −3 and x = 6, x-intercepts at (−4, 0) and (1, 0),horizontal asymptote at y = −2
*My previous answers have been -2 x^2-3x-4/x^2+9x+18. and -2 x^2-3x-4/x^2+3x-18.
Can someone explain where I am going wrong? Thank you.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Since f has a vertical is at x+=-3, and x=6 then the denominator of the rational function contains the term %28x+%2B3%29 and x-6.
Function f has the form.

f%28x%29+=+g%28x%29+%2F+%28%28x%2B3%29+%28x-6%29%29
since has a horizontal asymptote y=-2, x-intercepts %28x%2B4%29 and %28x-1%29, g%28x%29 contains
f%28x%29+=+%28-2%28x%2B4%29+%28x-1%29%29+%2F+%28%28x%2B3%29+%28x-6%29%29