y=-5/x-7 Graph the function. State the domain and range.

The given function y = 5/x-7 is the same as:
y = 5/x-(7x)/x
y = (5-7x)/x or y =(-7x+5)/x.
To be able to graph the rational function y =(-7x+5)/x , 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 =(-7x+5)/x , the D(x) =x.
Then, D(x) =0 will be x=0 .
The vertical asymptote exists at x=0.
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 =(-7x+5)/x , the leading terms are   ax^n=-7x or -7x^1 and bx^m=x or x^1 . The values n =1 and m=1 satisfy the condition: n=m. Then, horizontal asymptote  exists at y=(-7)/1 or y =-7 .
To solve for possible y-intercept, we plug-in x=0 and solve for y.
y =(-7*0+5)/0
y = 5/0  
y = undefined
Thus, there is no y-intercept.
To solve for possible x-intercept, we plug-in y=0 and solve for x .
0 =(-7x+5)/x
0*x =(-7x+5)/x*x
0 =-7x+5
0-5=-7x+5-5
-5=-7x
(-5)/(-7)=(-7x)/(-7)
x=5/7 or 0.714  (approximated value)
Then, x-intercept is located at a point (0.714,0) .
Solve for additional points as needed to sketch the graph.
When x=1 , the y = (-7*1+5)/1=(-2)/1=-2 . point: (1,-2)
When x=5 , the y =(-7*5+5)/5=(-30)/5=-6 . point: (5,-6)
When x=-1 , the y =(-7*(-1)+5)/(-1) =12/(-1)=-12 . point: (-1,-12)
When x=-5 , the  y =(-7*(-5)+5)/(-5) =40/(-5)=-8 . point: (-5,-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, 0)uu(0,oo) and range: (-oo,-7)uu(-7,oo) . 
The domain of the function is based on the possible values of x . The x=0 excluded due to the vertical asymptote.
The range of the function is based on the possible values of y. The y=-7 is excluded due to the horizontal asymptote.