let fxx2x1 carefully sketch the graph yfx make sure to show

let f(x)=(x+2)/(x-1) carefully sketch the graph y=f(x) make sure to show your work and label coordinates of all intercepts and then explicit equations of all the asymptotes

Solution

f(x)=(x+2)/(x-1)

x intercept is

x+2=0

x=-2

(-2,0)

y intercept is

f(0)=2/-1=-2

(0,-2)

Vertical asymptote

x-1=0

x=1

Horizontal asymptote

Numerator and denominator have same degree, therefore horizontal asymptote is y= numerator\'s leading coefficient/denominator\'s leading coefficient

y=1/1=1