What is the domain and range of the given function #f(x)= (x-1)/(x+3)#?

1 Answer
Feb 18, 2017

Answer:

Domain: #(-oo, -3) U (-3, oo)#
Range: #(-oo, 1) U (1, oo)#

Explanation:

Rational function: #(N(x))/(D(x)) = (x-1)/(x+3)#:

Analytically, vertical asymptotes are found when you set #D(x)=0#:

#x + 3 = 0#; #x = -3# so the vertical asymptote is at #x = -3#

Horizontal asymptotes are found based on the degree of the functions: #(ax^n)/(bx^m)# When #n=m, y=a/b = 1#

so the horizontal asymptote is at #y = 1#

You can see this from the graph:
graph{(x-1)/(x+3) [-10, 10, -5, 5]}