Finding Horizontal Asymptotes Finding Horizontal Asymptotes Before going to study anything about Finding Horizontal Asymptotes in this article, we will first discuss some important facts about the horizontal asymptotes and we will try to compare the horizontal asymptotes and the vertical asymptotes then after that we will be finding horizontal asymptotes by taking some of the good examples related to the topic because if we know in detail about the horizontal asymptotes and their variability when they are being compared with the vertical asymptotes, it will help us very much in finding horizontal asymptotes of any functions which will be given in the example. So let us now discuss some of the facts about the horizontal asymptotes. A value which is occurring on the y axis of the coordinate system and is being approached by the function but the function is never able to reach that value in real is the horizontal asymptote of that function. Now we will compare some of the properties of the horizontal asymptotes with those of the vertical asymptotes.
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The horizontal asymptotes are only the helpful suggestions unlike the vertical asymptotes. Though we cannot ever be able to touch any of the vertical asymptotes but we can very readily touch the horizontal asymptotes and not only touch we can also be able to cross any of the horizontal asymptotes. It should be noticed that the vertical asymptotes generally react very particularly in the graph when they come near the origin ( 0 , 0 ) but unlike them the horizontal asymptotes are the one which just show the regular behavior and that too very far towards the sides of any of the graph. So we have now understood enough about the horizontal asymptotes as required for finding horizontal asymptotes and we have also compared the horizontal asymptotes and the vertical asymptotes. Thus we will now see some of the steps which we need to follow in finding horizontal asymptotes of any function given in any question. For finding horizontal asymptotes the first step which we have to perform is that we have to change the function in such a way that the function comes into a form which is standard for it. Then the next step which we have to follow for finding horizontal asymptotes of any function is to vanish every term which is present in the denominator or present in the numerator leaving some of the terms of the x which contain the maximum exponent. After applying these 2 steps for finding horizontal asymptotes we will very easily get the horizontal asymptote. Thus we have seen in the above paragraph that finding horizontal asymptotes is very easy and we just have to perform 2 steps for finding horizontal asymptotes.
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So let us take an example know in which we will be finding horizontal asymptotes of the function g ( x ) = [ ( 4x – 1 ) . ( x – 5 ) ] / [ x . ( x – 6 ) ]. For finding horizontal asymptotes of this function we will first write the function as g ( x ) = ( 4x2 – 21x + 5 ) / ( x2 – 6x ). So the horizontal asymptote of the given function is y = 4x2 / x2 that is y = 4.
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