Question 1045715: I am a rational function having a vertical asymptote at
the lines x = 3 and x = -3, and a horizontal asymptote y = 1.
If my only x-intercept is 5, and y-intercept is -5/9, What
function am I?
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website! I am a rational function having a vertical asymptote at
the lines x = 3 and x = -3, and a horizontal asymptote y = 1.
If my only x-intercept is 5, and y-intercept is -5/9, What
function am I?
Since it has vertical asymptotes at the lines x = 3 and x = -3, the
denominator is (x-3)(x+3) or x²-9
Since it has horizontal asymptote y = 1, the leading term of the numerator
must by x²
So it has form:
   , for some B and C
Since it has x-intercept 5, it passes through the point (5,0),
so we substitute (x,y) = (5,0)
 
Multiply both sides by 16
Since it has y-intercept -5/9, it passes through the point (0,-5/9),
so we substitute (x,y) = (0,-5/9)
 
Multiply through by -9
 
Substitute in
 
 
So
becomes
Edwin
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