y=(x+6)/(4x-8) Graph the function. State the domain and range.

y=(x+6)/(4x-8)
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.
4x-8=0
4x=8
x=2
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 degree of the 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=1/4
Graph this horizontal asymptote on the grid. Its graph should be a dashed line. (See attachment.)
Next, find the intercepts.
y-intercept:
y=(0+6)/(4*0-8)=6/(-8)=-3/4
So the y-intercept is (0,-3/4) .
x-intercept:
0=(x+6)/(4x-8)
(4x-8)*0=(x+6)/(4x-8)*(4x-8)
0=x+6
-6=x
So, the function has an x-intercept (-6,0) .
Also, determine the other points of the function. To do so, assign any values to x, except 1. And solve for the y values.
x=-10, y=(-10+6)/(4(-10)-8)=(-4)/(-48)=1/12
x=-3, y=(-3+6)/(4(-3)-8)=3/(-20)=-3/20
x=1, y=(1+6)/(4(1)-8)=7/(-4)=-7/4
x=3, y=(3+6)/(4(3)-8)=9/(4)=9/4
x=5, y=(5+6)/(4(5)-8) = 11/12=11/12
x=6, y=(6+6)/(4(6)-8)=12/16=3/4
x=10, y=(10+6)/(4(10)-8)=16/32=1/2
Then, plot the points (-10,1/12) ,   (-6,0) ,   (-3,-3/20) ,    (0,-3/4) ,   (1,-7/4) ,   (3,9/4) ,   (5,11/12) ,   (6,3/4) , and (10,1/2) .
And connect them.
Therefore, the graph of the function is:

Base on the graph, the domain of the function is (-oo, 2) uu(2,oo) . And its range is (-oo, 1/4) uu (1/4, oo) .