# `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)` .