Question

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

Answer 1

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]}