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

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Answer 1 · 2015-03-02T11:36:28

The answer is: #x!=3#, because the denominator cannot be zero.

#dom(f)=(-∞,3)∪(3,+∞)#

Answer 2 · 2016-12-02T09:48:45

The domain of the dependent variable is the spread of the variable on which it depends.
Here, the domain is #x in ( -oo, oo)#, sans x = 3

By actual division,

#f(x) = 1+12/(x-3)#

As #x to 3, y to +-oo#.

As #x to +-oo, 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]}