y=10/(x+7)-5 Graph the function. State the domain and range.

The given function y = 10/(x+7)-5 is the same as:
y =10/(x+7)-5(x+7)/(x+7)
y=10/(x+7)-(5x+35)/(x+7)
y=(10-(5x+35))/(x+7)
y=(10-5x-35)/(x+7)
y = (-5x-25)/(x+7)
To be able to graph the rational function y = (-5x-25)/(x+7) , 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 =(-5x-25)/(x+7) , the D(x)=x+7 .
Then, D(x) =0  will be:
x+7=0
x+7-7=0-7
x=-7
The vertical asymptote exists at x=-7 .
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 =(-5x-25)/(x+7) , the leading terms are ax^n=-5x or -5x^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=-5/1 or y =-5 .
To solve for possible y-intercept, we plug-in x=0 and solve for y .
y =(-5*0-25)/(0+7)
y =(-25)/7
y = -25/7 or -3.571  (approximated value)
Then, y-intercept is located at a point (0, -3.571) .
To solve for possible x-intercept, we plug-in y=0 and solve for x .
0 =(-5x-25)/(x+7)
0*(x+7) =(-5x-25)/(x+7)*(x+7)
0 =-5x-25
0+5x=-5x-25+5x
5x=-25
(5x)/5=(-25)/5
x=-5
Then, x-intercept is located at a point (-5,0).
Solve for additional points as needed to sketch the graph.
When x=3, the y = (-5*3-25)/(3+7)=-40/10=-4. point: (3,-4)
When  x=-6 , the y = (-5(-6)-25)/(-6+7)=5/1=5 . point: (-6,5)
When x=-9 , the y =(-5(-9)-25)/(-9+7)=20/(-2)=-10 . point: (-9,-10)
When x=-12 , the y = (-5(-12)-25)/(-12+7)=35/(-5)=-7 . point: (-12,-7)
 
As shown on the graph attached, the domain: (-oo, -7)uu(-7,oo) and range: (-oo,-5)uu(-5,oo) . 
The domain of the function is based on the possible values of x. The x=-7 excluded due to the vertical asymptote.
The range of the function is based on the possible values of y . The y=-5 is excluded due to the horizontal asymptote.