Question

Sketch the asymptotes and graph the function y=6/(x-2)+4

Answer 1

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 2

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
`y = (6x^(0) )/((x^(1)-2))`

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.