Question

Find the domain and range of: f(x) = 4 / (x+2)

Answer 1

I know the denominator can't equal -2 but the book says the answer is (-infinity, -2) U (-2, infinity) and I don't understand that.

Answer 2

\[f(x)=\frac{ 4 }{ x+2 }\]

The domain is all the values for x that will give you a return f(x) value. You are right, for this function if the denominator is zero then f(x) is not defined. This occurs when x=-2

Answer 3

That is the only problem with this function... x can be anything but -2.

Domain-- all x, such that x does not equal -2.

Answer 4

Oh, wait. I think I'm starting to understand it a bit better. If you graph it you would go from -infinity and have to stop before -2, and then just after -2 continue towards infinity. What I'm confused on is that question is asking for range too.

Answer 5

@DanJS

Answer 6

Oh shoot, I actually misread the question. It just wants the domain. That's why the book wasn't listing the range as part of the answer. Sorry, I'm really tired and can't think straight aha.

Answer 7

Right, think of what happens to f(x) as you put in values that are closer and closer to x=-2..

The denominator is getting smaller and smaller as x gets closer and closer to -2. The function will become larger and larger as the denominator gets smaller.

Answer 8

The graph goes off to infinities as you approach x=-2, and x=-2 does not exist.