SOLUTION: Write an equation for a rational function with: Vertical asymptotes at x = −4 and x = −2 x intercepts at (−6,0) and (−3,0) y intercept at (0,3)

Algebra ->  Rational-functions -> SOLUTION: Write an equation for a rational function with: Vertical asymptotes at x = −4 and x = −2 x intercepts at (−6,0) and (−3,0) y intercept at (0,3)       Log On


   

Question 1178199: Write an equation for a rational function with:
Vertical asymptotes at x = −4 and x = −2

x intercepts at (−6,0) and (−3,0)
y intercept at (0,3)
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Vertical asymptotes at x = −4 and x = −2:

Factors of (x+4) and (x+2) in the denominator

x intercepts at (−6,0) and (−3,0):

Factors of (x+6) and (x+3) in the numerator

So the equation is of the form

%28a%28x%2B6%29%28x%2B3%29%29%2F%28%28x%2B4%29%28x%2B2%29%29
y intercept at (0,3):

Solve f(0)=3 to find the constant factor a

%28a%286%29%283%29%29%2F%28%284%29%282%29%29+=+3
18a%2F8+=+3
18a+=+24
a+=+24%2F18+=+4%2F3

ANSWER: %28%284%2F3%29%28x%2B6%29%28x%2B3%29%29%2F%28%28x%2B4%29%28x%2B2%29%29