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

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

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.

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x