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Question 362319: Find an equation of a rational function f that satisfies the conditions:
vertical asymptote: x = - 3, x = 0
horizontal asymptote: y = 0
x-intercept: 1; f (2) = 1
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find an equation of a rational function f that satisfies the conditions:
vertical asymptote: x = - 3, x = 0
implies factors of (x+3) and x in the denominator
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horizontal asymptote: y = 0
implies the degree of the numerator is less than the degree
of the denominator.
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x-intercept: 1; f (2) = 1
Implies it passes thru (1,0) and (2,1)
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Form: y = (ax+b)/[x(x+3)]
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0 = (a+b)/[1(1+3)]
and
1 = (2a+b)/[2(2+3)]
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Simplify to solve for a and b:
a + b = 0
2a+b = 10
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Subtract 1st from 2nd and solve for "a":
a = 10
Then b = -10
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Equation:
y = (10x-10)/[x(x+3)]
or
y = [10(x-1)]/[x(x+3)]
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Cheers,
Stan H.
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