SOLUTION: create a rational function with a vertical asymptotes x=±1 and oblique asymptote of y=2x-3 and y-intercept of 4

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Question 728570: create a rational function with a vertical asymptotes x=±1 and oblique asymptote of y=2x-3 and y-intercept of 4
Answer by KMST(5347) About Me  (Show Source):
You can put this solution on YOUR website!
y=2x-3%2B7%2F%28x%5E2-1%29=%282x%5E3-3x%5E2-2x-4%29%2F%28x%5E2-1%29 graph%28300%2C300%2C-5%2C5%2C-15%2C10%2C2x-3%2C2x-3-7%2F%28x%5E2-1%29%29
If we add to y=2x-3 a term f%28x%29 such that lim%28+x-%3Einfinity%2C+f%28x%29+%29+=0 ,
we get a function that has y=2x-3 for an asymptote.
Since we want y=4 for x=0 (y-intercept=4),
we need
2%2A0-3%2Bf%280%29=4 --> -3%2Bf%280%29=4 --> f%280%29=4%2B3=7
g%28x%29=1%2F%28%28x%2B1%29%28x-1%29%29=1%2F%28x%5E2-1%29 is a function with vertical asymptotes {x=-1}}} and x=1 and
lim%28+x-%3Einfinity%2C1%2F%28x%5E2-1%29%29+=0 .
g%28x%29 is promising, but g%280%29=-1 ,
so we use f%28x%29=-7g%28x%29 which makes f%280%29=-7%2A%28-1%29=7.