How do you find the domain and range of $f(x) = (x-4)/(x+3)$ ?

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Answer 1 · 2017-03-07T22:55:43

The domain is $x!=-3$ as this would make the denominator $=0$ .
There are no other restrictions.

For the range we look at what happens when $x->+-oo$
In both cases the fraction will approach $f(x)=+1$ , but will never get there. $y!=+1$

In short:
$lim_(x->-3^-)f(x)=+oo$ and $lim_(x->-3^+)f(x)=-oo$

$lim_(x-> -oo)f(x)=lim_(x->+oo)f(x)=+1$

$x=-3$ and $y=+1$ are called the asymptotes .
graph{(x-4)/(x+3) [-25.65, 25.65, -12.82, 12.84]}

How do you find the domain and range of f(x) = (x-4)/(x+3) f(x) = (x-4)/(x+3) ?