Question: I have a quarter 1 test tomorrow and I have looked on many websites containing set builder notation to find domain and range but I still don't understand. Is there anyway to remember it or even how to do it??

Answer: 
I'm going to make some assumptions, let me know if this is what you have in mind.

Suppose we are given this graph:

[![enter image description here](https://i.stack.imgur.com/g1mmK.png)](https://i.stack.imgur.com/g1mmK.png)

and we are asked to give the domain and range of the function in set builder notation.

We can see that the function has a value at all points except where $x = 0$. So the domain of the function is $\{ x \in \mathbb{R} : x \neq 0 \} $

Now we will consider the range. Note that the function goes off to $\pm\infty$ near the origin, so most values are in the range of the function. However, this particular function never crosses the x-axis,
so 0 is not in the range. Therefore, the range is $\{ y \in \mathbb{R} : y \neq 0 \}$.

In all questions of this form, you have to first: identify the domain and range, and second: write it in set-builder notation. You can think about finding the range by imagining horizontal lines and seeing at what y-values they do (and do not) intersect the graph. Likewise with horizontal lines for the domain.
Going off the comment, I assume you want to know how to give the domain and range of a function *using* set builder notation. For a given function $f(x)$, you can think of the domain as everything that you can put into the function, and the range as everything that you can get out of the function. For example, if we have a line of the form $y = 5x + 2$, then the domain would be all the possible values you can put in for $x$, and the range would be all output $y$ values. Now, in this case, the domain is all real numbers, as you can put in any $x$, and the output is also all reals, as $y$ can take on any value on the real line. In this case, the domain and range would just be $\mathbb{R}$, the set of all real numbers. 

Consider a different function like $y = \sqrt{x}$. The square root is not defined for negative numbers, so we have to restrict the domain. So the domain would be $\{x : x \geq 0\}$. Similarly, the range is only non-negative numbers, so the range would be the same set. The idea is that you can use this notation to describe precisely the set of possible "inputs" and "outputs" for your given function.