# What is the domain of the function f(x)=(x+9)/(x-3)?

Mar 2, 2015

The answer is: $x \ne 3$, because the denominator cannot be zero.

dom(f)=(-∞,3)∪(3,+∞)

Dec 2, 2016

The domain of the dependent variable is the spread of the variable on which it depends.
Here, the domain is $x \in \left(- \infty , \infty\right)$, sans x = 3

#### Explanation:

By actual division,

$f \left(x\right) = 1 + \frac{12}{x - 3}$

As $x \to 3 , y \to \pm \infty$.

As $x \to \pm \infty , y \to 1$.

Likewise, the range of f is (-oo, oo)#, sans f = 1.

The lines x = 3 and y =1 are called asymptotes to the graph y = f(x)

graph{y(x-3)-x-9=0 [-80, 80, -40, 40]}