Horizontal Asymptotes

 

Horizontal Asymptotes


 Many graphs, especially exponential graphs have asymptotes. Asymptotes are curves that do not touch a line but go really close to it. In the graph of y=2^x, the line y=0 is an asymptote as the graph doesnt touch it but keeps going closer to it till infinity.



Horizontal asymptotes are asymptotes that are horizontally placed, in the graph of y=2^x, the asymptote y=0 is a horizontal asymptote!

To find the horizontal asymptote of an equation, we need to consider only the values with the highest degree of x in the numerator and the denominator. The highest degree of x is the x value with the highest power.

Worked Examples:

Here 'M' has a degree of 2 while the highest degree in the numerator is just 1. So as M>N, there is no horizontal asymptote.



Here 'M' is 0 and 'N' is 1, since M<N, the horizontal asymptote is y=0



Here both M and N have a degree of 1. So we divide the coeefficients and get 2/6=1/3, the horizontal asymptote therfore is y=1/3


Questions:

Solution:
y=4

                                                                  Solution:
                                                                      y=1


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