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For some rational function  f(x), the graph of y=f(x) has an oblique asymptote of y=5x+7. Enter the equation of the horizontal asymptote of the graph of

 

 Apr 18, 2020
 #1
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 Apr 18, 2020
 #2
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If  f(x)  were a function like:  f(x)  =  (5x2 + 2x + 8) / (x - 1)  it would have an oblique asymptote of  y  = 5x + 7.

 

This would make the final function:  y  =  [ (5x2 + 2x + 8) / (x - 1) ] / (x - 2)

and would simplify to:                       y  =  (5x2 + 2x + 8) / [ (x - 1)(x - 2) ]

or:                                                     y  =  (5x2 + 2x + 8) / (x2 - 3x + 2)

which would have an horizontal asymptote of  y  =  5.

 

Now, this is just an example, but I believe that this would be true for all examples, so the equation of the horizontal

asymptote woulld always be:  y  =  5.

 Apr 19, 2020

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