1. Domain and Range

Alright, I'm having trouble with these concepts.

Well, figuring out the range. I've used like three books and haven't really understood it.

I know how to find out the domain. It'll either be like any real number or like -3 less than or equal to 0 less than or equal to 3. Something like that.

But the range, I think, you can find on the y-axis. Like say that example and the function or line crosses the y-axis at 0. How would I write that?

2. Domain is essentially what values are applicable(valid) for x.

Ex: $\displaystyle \frac{x + 1}{x - 1}$
In this case the domain is:
$\displaystyle x = \epsilon$ (All real numbers)
$\displaystyle x \ne 1$

There is a vertical asymptote at 1.

Range is essentially what values are applicable(valid) for y.

Ex: $\displaystyle \frac{x + 1}{x - 1}$
In this case the domain is:
$\displaystyle y = \epsilon$ (All real numbers)
$\displaystyle y \ne 1$

There is a horizontal asymptote at 1.

Domain of a function - Wikipedia, the free encyclopedia
Range (mathematics) - Wikipedia, the free encyclopedia

3. Well, what if there isn't anything like that? I know how to do it like that.

Like the picture I posted. It's just a graph and I'm suppose to find the range.

4. On your graph specifically we can see that x extends in the negative and positive direction infinitely.
So the domain of x: $\displaystyle x = \epsilon$ (All real numbers)

Similar problem for the range. On your graph (I can't really see the markings on the graph) but I'm assuming it's a sin function.
For simplicities sake I'm going to assume it's: $\displaystyle f(x) = sinx$

That means that the range of y is simply the range of the function: $\displaystyle f(x) = sinx$. And the range is: $\displaystyle |y| \le 1$

Now, on your graph, you have to check what numbers it's oscillating between.

5. Originally Posted by eXist
On your graph specifically we can see that x extends in the negative and positive direction infinitely.
So the domain of x: $\displaystyle x = \epsilon$ (All real numbers)

Similar problem for the range. On your graph (I can't really see the markings on the graph) but I'm assuming it's a sin function.
For simplicities sake I'm going to assume it's: $\displaystyle f(x) = sinx$

That means that the range of y is simply the range of the function: $\displaystyle f(x) = sinx$. And the range is: $\displaystyle |y| \le 1$

Now, on your graph, you have to check what numbers it's oscillating between.
Well, it's between -5 and 5 and it might very well be a sinx whatever, but I don't think that's how it's written yet. This is just a College Algebra problem. On the graph on the y-axis the lowest and highest points would be -1 and 1.

6. If the graph shows restrictions on x (like you said between -5 and 5) mark it that way. Same thing for y .