y=(x-1)/(x+5) Graph the function. State the domain and range.

y=(x-1)/(x+5)
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+5=0
x=-5
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 the degree of numerator and denominator.
degree of numerator = 1
degree of the denominator = 1
Since they have the same degree, the asymptote is horizontal. To get the equation of HA, divide the leading coefficient of numerator by the leading coefficient of the denominator.
y=1/1
y=1
Graph this horizontal asymptote on the grid. Its graph should be a dashed line.(See attachment.)
Next, find the intercepts.
y-intercept:
y=(0-1)/(0+5)
y=-1/5
So the y-intercept is  (0, -1/5) .
x-intercept:
0=(x-1)/(x+5)
(x+5)*0=(x-1)/(x+5)*(x+5)
0=x-1
1=x
So, the x-intercept is (1,0) .
Also, determine the other points of the function. To do so, assign any values to x, except -5. And solve for the y values.
x=-15, y=(-15-1)/(-15+5) = (-16)/(-10)=8/5
x=-11, y=(-11-1)/(-11+5)=(-12)/(-6)=2
x=-7, y=(-7-1)/(-7+5)=(-8)/(-2)=4
x=-6, y=(-6-1)/(-6+5)=(-7)/(-1)=7
x=-3, y=(-3-1)/(-3+5) = (-4)/2=-2
x=4, y=(4-1)/(4+5)=3/9
x=15, y=(15-1)/(15+5)=14/20=7/10
Then, plot the points (-15,8/5) ,   (-11,2) ,   (-7,4) ,   (-6,7) ,   (-3,-2) ,   (0,-1/5) ,   (1,0) ,   (4,3/9) and (15,7/10) .
And connect them.
Therefore, the graph of the function is:

Base on the graph, the domain of the function is (-oo, -5) uu (-5,oo) . And its range is (-oo, 1) uu (1,oo) .