y=6/(x-1) Graph the function. State the domain and range.

y=6/(x - 1)
First, determine the vertical asymptote of the rational function. Take note that vertical asymptote refers to the values of x that make the function undefined. Since it is undefined when the denominator is zero, to find the VA, set the denominator equal to zero.
x - 1 = 0
x=1
Graph this vertical asymptote on the grid. Its graph should be a dashed line. (See attachment.)
Next, determine the horizontal or slant asymptote. To do so, compare degree of the numerator and denominator.
y=6/(x-1)
degree of numerator = 0
degree of the denominator = 1
Since the degree of the numerator is less than the degree of the denominator, the asymptote is horizontal, not slant.  And its horizontal asymptote is:
y=0
Graph this horizontal asymptote on the grid. Its graph should be a dashed line.(See attachment.)
Next, find the intercepts.
y-intercept:
y=6/(0-1)=-6
So the y-intercept is (0,-6)
x-intercept:
0=1/(x-6)
(x-6)*0 = 1/(x-6)*(x-6)
0=1
So, the function has no x-intercept.
Also, determine the other points of the function. To do so, assign any values to x, except 1. And solve for the y values.
x=-10 , y=6/(-10-1)=-6/11
x=-5 , y=6/(-5-1)=-1

x=-1 , y=6/(-1-1)=-3
x=2 , y=6/(2-1)=6
x=3 , y=6/(3-1)=3
x=5 , y=6/(5-1)=3/2
x=10 , y=6/(10-1)=2/3
Then, plot the points (-10,-6/11) ,   (-5,-1) ,   (-3,-3/2) ,   (-1,-3) ,   (0,-6) ,   (2,6) ,   (3,3) ,   (5,3/2) ,   and   (10,2/3) . 
And connect them.
Therefore, the graph of the function is:

Base on the graph, the domain of the function is (-oo,1) uu (1,oo) .  And its range is (-oo, 0) uu (0,oo).