# `y=6/(x-1)` Graph the function. State the domain and range.

`y=6/(x - 1)`

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 - 1 = 0`

`x=1`

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.

`y=6/(x-1)`

degree of numerator = 0

degree of the denominator = 1

Since the degree of the numerator is less than the degree of the denominator, the asymptote is horizontal, not slant.  And its horizontal asymptote is:

`y=0`

Graph this horizontal asymptote on the grid. Its graph should be a dashed line.(See attachment.)

Next, find the intercepts.

y-intercept:

`y=6/(0-1)=-6`

So the y-intercept is (0,-6)

x-intercept:

`0=1/(x-6)`

`(x-6)*0 = 1/(x-6)*(x-6)`

`0=1`

So, the function has no x-intercept.

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=6/(-10-1)=-6/11`

`x=-5` , `y=6/(-5-1)=-1`

` `

`x=-1` , `y=6/(-1-1)=-3`

`x=2` , `y=6/(2-1)=6`

`x=3` , `y=6/(3-1)=3`

`x=5` , `y=6/(5-1)=3/2`

`x=10` , `y=6/(10-1)=2/3`

Then, plot the points `(-10,-6/11)` ,   `(-5,-1)` ,   `(-3,-3/2)` ,   `(-1,-3)` ,   `(0,-6)` ,   `(2,6)` ,   `(3,3)` ,   `(5,3/2)` ,   and   `(10,2/3)` .

And connect them.

Therefore, the graph of the function is:

Base on the graph, the domain of the function is `(-oo,1) uu (1,oo)` .  And its range is `(-oo, 0) uu (0,oo)`.