Question 551137: Im taking pre calc as an online class and I'm in way over my head because they do not teach it in a way that I can understand AT ALL. please help,
I need to know the vertical, horizontal, and slant asymtotes for:
I have an idea on how to get the vertical and horizontal but I just wish I had an easier less confusing, faster way to determine the slant
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! I have an idea on how to get the vertical and horizontal but I just wish I had an easier less confusing, faster way to determine the slant
(2x^3+24x^2+35x-175)/(x^2+14x+45)
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For rational functions, when the degree of the numerator is equal to or less than the degree of the denominator, you will have vertical and horizontal asymptotes, which you say you understand. Slant asymptotes come into the picture when the degree of the numerator is one degree higher than that of the denominator. To find the equation of the slant asymptote, divide the numerator by the denominator by long division. The quotient will be a first degree equation of a straight line which is the slant asymptote. As you can see, the remainder will approach zero as x approaches infinity. At your level, I believe you know how to do long division, so I will let you do it for the given rational function which has a slant asymptote.
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