y=-3/(x-4)-1 Graph the function. State the domain and range.

The given function y = -3/(x-4)-1 is the same as:
y = -3/(x-4)-1*(x-4)/(x-4)
y = -3/(x-4)-(x-4)/(x-4)
y=(-3-(x-4))/(x-4)
y=(-3-x+4)/(x-4)
y = (-x+1)/(x-4)
To be able to graph the rational function  y = (-x+1)/(x-4) , we solve for possible asymptotes.
Vertical asymptote exists at x=a that will satisfy D(x)=0 on a rational function f(x)= (N(x))/(D(x)) . To solve for the vertical asymptote, we equate the expression at denominator side to 0 and solve for x .
In y = (-x+1)/(x-4), the D(x)=x-4.
Then, D(x) =0  will be:
x-4=0
x-4+4=0+4
x=4
The vertical asymptote exists at  x=4 .
To determine the horizontal asymptote for a given function: f(x) = (ax^n+...)/(bx^m+...) , we follow the conditions:
when n lt m     horizontal asymptote: y=0
        n=m        horizontal asymptote: y =a/b
        ngtm       horizontal asymptote: NONE
In y = (-x+1)/(x-4) , the leading terms are ax^n=-x or -1x^1 and bx^m=x or 1x^1 . The values n =1 and m=1 satisfy the condition: n=m. Then, horizontal asymptote  exists at y=(-1)/1 or y =-1 .
To solve for possible y-intercept, we plug-in x=0 and solve for 
y =(-0+1)/(0-4)
y =1/(-4)
y = -1/4 or -0.25
Then, y-intercept is located at a point (0, -0.25).
To solve for possible x-intercept, we plug-in y=0 and solve for x .
0 =(-x+1)/(x-4)
0*(x-4)= (-x+1)/(x-4)*(x-4)
0 =-x+1
x=1
Then, x-intercept is located at a point (1,0)
Solve for additional points as needed to sketch the graph.
When x=3 , the y =(-3+1)/(3-4)=-2/(-1)=2 . point: (3,2)
When x=5 , the y = (-5+1)/(5-4)=(-4)/1=-4 . point: (5,-4)
When x=7 , the y =(-7+1)/(7-4)=(-6)/3=-2 . point: (7,-2)
When x=-2 , the y =(-(-2)+1)/(-2-4)=3/(-6)=-0.5 . point: (-2,-0.5)
Applying the listed properties of the function, we plot the graph as:

You may check the attached file to verify the plot of asymptotes and points.
As shown on the graph, the domain: (-oo, 4)uu(4,oo)
and range: (-oo,-1)uu(-1,oo) . 
The domain of the function is based on the possible values of x. The x=4 excluded due to the vertical asymptote.
The range of the function is based on the possible values of y . The y=-1 is excluded due to the horizontal asymptote.