h(x)=11/(x-9)+9 Graph the function. State the domain and range.

The given function h(x)= 11/(x-9)+9 is the same as:
h(x)= 11/(x-9)+9 *(x-9)/(x-9)
h(x)= 11/(x-9)+(9x-81)/(x-9)
h(x)=(11+(9x-81))/(x-9)  
h(x)=(11+9x-81)/(x-9)
h(x) = (9x-70)/(x-9)
To be able to graph the rational function h(x) =(9x-70)/(x-9) or y =(9x-70)/(x-9) , we solve for possible asymptotes. Note: h(x)=y .
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 h(x) =(9x-70)/(x-9) , the D(x)=x-9.
Then, D(x) =0  will be:
x-9=0
x-9+9=0+9
x=9
The vertical asymptote exists at x=9 .
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 h(x) = (9x-70)/(x-9) , the leading terms are ax^n=9x or 9x^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=9/1 or y =9.
To solve for possible y-intercept, we plug-in x=0 and solve for y.
y =(9*0-70)/(0-9)
y =(-70)/(-9)
y = 70/9 or 7.778 (approximated value)
Then, y-intercept is located at a point (0, 7.778).
To solve for possible x-intercept, we plug-in y=0 and solve for x.
0 =(9x-70)/(x-9)
0*(x-9)= (9x-70)/(x-9)*(x-0)
0 =9x-70
0+70=-9x-70+70
70=9x
70/9=(9x)/9
x=70/9 or 7.778
Then, x-intercept is located at a point (7.778,0).
Solve for additional points as needed to sketch the graph.
When x=8, the y = (9*8-70)/(8-9)=2/(-1)=-2 . point: (8,-2)
When x=10 , the y = (9*10-70)/(10-9)=20/1=20 . point: (10,20)
When x=20 , the y =(9*20-70)/(20-9)=110/11=10 . point: (20,10)
When x=-2 , the y =(9*(-2)-70)/(-2-9)= (-88)/(-11)=8 . point: (-2,8)
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, 9)uu(9,oo)
and range: (-oo,9)uu(9,oo).
The domain of the function is based on the possible values of x. The x=9 is excluded due to the vertical asymptote.
The range of the function is based on the possible values of y . The y=9 is excluded due to the horizontal asymptote.