Horizontal Asymptote Horizontal Asymptote This article is basically written to understand the method to Find Horizontal Asymptote. But before going to see that how to find horizontal asymptote we will first try to understand the meaning of the term horizontal asymptote. The horizontal asymptote is the value on the y axis which any function try to reach out but it does not really get there. Now we have understood what a horizontal asymptote actually means. So now we will study about how to find horizontal asymptote. To find horizontal asymptote, we should first try to convert the function into a form which is standard. The horizontal asymptotes are made when the graph of the function is extended for ever either to the left side or to the right side. Through the fact given in the last line, we try to say that we were seeing for very high negative values of the x or very high positive values of the x.
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Before taking any of the examples of how to find horizontal asymptote, let us first remind the steps which are followed to find horizontal asymptote. Primarily there are two steps which need to be performed when we have to find horizontal asymptote. Out of those two steps the first step is as follows. We have to convert the function or the equation into a form which is standard. And the second step to find horizontal asymptote is as follows. Every single thing needs to be removed by us other than the exponents of the x which are the biggest from the denominator and the numerator. Now let us take some examples in which we have to find horizontal asymptote. Let us take first example in which we have to find horizontal asymptote of the function which is as follows: g ( x ) = [ 3x3 – 3 ] / [ 4x3 – 12 ]. The first step which we have to perform to find horizontal asymptote is to find out about the fact that how the function given in the example reacts when x becomes large. For finding that how the above function will behave when we will take x to infinity we will first take the terms in the denominator and the terms in the numerator which come out to be dominant. Before going further we should try to understand the meaning of the term dominant. The terms which are dominant are the terms which have the highest exponents. Also we will notice that when x reaches to the infinity, all the terms other than the terms which are dominant have critically no meaning.
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But in this example the exponents of the numerator and the exponents of the denominator are equal because we observe in the above example the terms which are dominant in the numerator and the denominator both possess an exponent equal to 3. So after removing the other terms we get g ( x ) = 3x3 / 4x3 = 3 / 4. So in this example 3 / 4 comes out to be the horizontal asymptote of the function given in the example. However the horizontal asymptote must be expressed in the form y = 3 / 4.
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