Posted by I Need Help on Sunday, April 11, 2010 at 12:47pm.
Design a rational function with the following characteristics: three real zeros, one of multiplicity 2; yintercept 1; vertical asymptotes x=2 and x=3; oblique asymptote y=2x+1.

Math  Damon, Sunday, April 11, 2010 at 1:30pm
Well first lets get one with three real zeros.
y = k(xx1)(xx2)(xx3)
but one happens twice
y = k(xx1)(xx2)(xx2)
denominator = 0 at x=2 and x = 3
y = c[(xx1)(xx2)(xx2)]/[(x+2)(x3)]
when x = 0, y = 1
y =1 = c[x1 x2^2]/6
6 = c x1 x2^2
when x and y are big, y = 2x
big x
y = c x^3/x^2 = c x
so c = 2
so
x1 x2^2 = 3 or x1 = x2^2/3
y = 2[(xx1)(xx2)(xx2)]/[(x+2)(x3)]
y = 2[(xx2^2/3)(xx2)(xx2)]/[(x+2)(x3)]
hmmm, unless I am missing something I am still free to choose x2

error  Damon, Sunday, April 11, 2010 at 1:43pm
x1 x2^2 = 3 or x1 = 3/x2^2
y = 2[(xx1)(xx2)(xx2)]/[(x+2)(x3)]
y = 2[(x  3/x2^2)(xx2)(xx2)]/[(x+2)(x3)]
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