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.

1.4

2.3

step-by-step explanation:

the formula for the constant of variation is

y= kx

divide each side by x

y/x =kx/x

y/x =k

we know a and y

1.   y/x = k

4/1 =4

check the other values to make sure they are the same

8/2 = 4   12/3 =4   and 16/4 =4  

the constant of variation is 4

2.   y/x = k

3/1 =3

check the other values to make sure they are the same

6/2 = 3   9/3 =3   and 12/4 =3  

the constant of variation is 3