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Question 466268: Find the equations of both the horizontal and vertical asymptotes of the rational function
f(x)= 2x^2+8/x-1
Answer:
Horizontal:
Vertical:
Show work or explain:
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find the equations of both the horizontal and vertical asymptotes of the rational function
f(x)= 2x^2+8/x-1
Answer:
Horizontal:
Vertical:
Show work or explain:
..
f(x)= 2x^2+8/x-1
To find the vertical asymptote, set the denominator=0, then solve for x.
x-1=0
x=1 (vertical asymptote)
..
horizontal asymptote:
When degree of numerator is less than degree of denominator, horizontal asymptote=x-axis or y=0.
When degree of numerator is equal to degree of denominator, divide coefficient of numerator by coefficient of denominator to get the horizontal asymptote.
When degree of numerator is one degree greater than that of denominator, you will get a slant asymptote, which is the case for given rational function. To find the slant asymptote, divide numerator by denominator. The quotient will be a straight-line function plus remainder. The straight-line function will be the slant asymptote.
..
2x^2+8/x-1
=2x+2+Remainder:(10/x-1)
slant asymptote, y=2x+2
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