Respuesta :

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There will be a vertical asymptote when the denominator approaches zero. So the vertical asymptote is about the line x=2.

There will be a horizontal asymptote as x approaches ±oo where the y value will approach 4.  So the horizontal asymptote is about the line y=4

Answer:

Step-by-step explanation:

We have to sketch the asymptotes of the given function y = 6/(x -2) + 4

1) For horizontal asymptotes

In the given function y = 6/(x -2) is in the form of [tex]y = \frac{6x^{0} }{(x^{1}-2)}[/tex]

Degree of x in numerator is lower than denominator therefore horizontal asymptote is y = 0

Since y = 6/(x -2) is shifted 4 upwards so horizontal asymptote for the shifted function will be y = 0+4 = 4

2) For vertical asymptotes

We will put the denominator of the function equal to the zero.

(x - 2) = 0

x = 2 is the vertical asymptote.

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