Do you know the "Vertical Line Test"? It's not really a technically brilliant plan, but it solve amny "function" problems. If you can see the graph, is there a vertical line that hits it twice? If not, it's a function.
Domain and Range - Well, first off, you can't have a function or a non-function without at at least two variables. This make the expression 11x^2 - 1 not really a candidate for Domain and Range, since it expresses no relationship. If we assume you mean y = 11x^2 - 1, then we can talk.
Domain is stuff that goes in.
Range is stuff that comes out.
It is often easier to hunt down what does NOT work.
If you really need help on all this for a quiz in the very near future, it is unlikely that this review will be of any value.