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

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Answer 1 · 2017-02-18T02:54:21

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

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]}

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