The range is the dependent variable, meaning it's dependent upon what you enter for the domain. That is, you have to enter something for the domain and solve it for the range.
So for like:
 = 3 - x)
if you plug in 2, then the range value is 1. If you plug in 6, the range value is -3.
If you need to find the entire range, i.e. all possibilities of what the range can be, for something linear like that, it's all real numbers.
The domain is the x. Since that is the independent variable, meaning you can put anything into that you like, the domain is any number that works and is not undefined in some way. If everything works, then it's all real numbers.
It's easier to learn what
doesn't work for the domain. What doesn't work for the domain is something that would make the equation undefined.
For example:
 = \frac{3}{x-1})
What makes a fraction undefined? Zero in the denominator. What x would make a zero? 1, because 1 - 1 = 0, and you end up with 0 in the denominator. Therefore, if x = 1, then it's undefined. Everything else works, because the
only thing that makes this undefined is when x - 1. So the domain is all real numbers except 1.
Don't know how complicated you're getting at this point. A variation on the above is if you had a quadratic in the denominator. Solving for what would give you zero is more involved of course, but it's the same concept. You can't have an x that would make the denominator zero.
Another example of something undefined is a negative under an even radical. For instance:
 = sqrt{x-1})
The answer under the radical cannot be negative. It
can be zero. But it can't be negative. x = 1 makes it zero, which is OK. x = 2 makes it 1, which is positive. Ah, but x = 0 is -1, which is a negative answer and makes it undefined. So the domain has to be equal to or greater than 1 - anything less than 1 won't work.
Basically, the domain is all real numbers unless you have something where certain x's would make it undefined.
Linear Mode
