Domain is what goes in, range is what comes out. Domain is x, range is y. Domain is left to right, range is bottom to top! Have an example of where you're confused? More on reddit.com

None of those require a calculator. Domain and range can be found by observing the function and it's inverse and finding out the points where it isn't defined. Exclude those points and you get the domain and range. Asymptotes are basically those points you excluded while finding the domain and range. x intercept is the point where y = 0 and y intercept is the point where x = 0. For any given question, all these barely takes 2-3 minutes with good practice. More on reddit.com

A function is a device where you give it an object and it gives you some other object back. The collection of objects that you're allowed to give it, or the objects that it can handle, is called the domain. Anything that the function can accept as an input is a member of this collection. The type of objects that the function gives you back is called the codomain. You should think of codomain as a collection of objects that give the "form" that an output can take. Not every object in the codomain will necessarily be an output of the function, these are only the various outputs that you could get. The collection of outputs that you actually do get back for some input is called the range (or image) of the function. The range is therefore a subcollection of the codomain. You'll notice I haven't said anything about numbers so far, and that's because the idea of functions isn't limited to sets of numbers. If you've done any programming, you'll recall that functions can take any sort of input and give back any sort of output, like numbers, lists, tuples, other functions, or user created types. In the context of your typical algebra course, you'll look at functions like f(x) = 2/(x-1) + 3. Here, the implication is that the domain is some subset of the real numbers, and you are often asked to determine exactly what subset it is, i.e. determine which numbers the function cannot accept as an input. The codomain is also implied to be the real numbers, and so that range is some subset of the real numbers. Again, you're often asked to determine what subset this is. For the function f I wrote above, the domain would be all real numbers except 1, since using 1 as an input would create a division by 0. The range will be all real numbers except 3, since the fraction above will never be zero. Lastly, I'll stress that the typical algebra course's mentality of first giving you a function defined by a formula and then asking you to find the domain and codomain/range is often (but not always) backwards. In many cases, you'll want to create a function for which you know exactly what inputs and outputs the function will have, and then determine some logical rule for the function to follow. This is done in programming all the time. You have to know what inputs you're dealing with before you can decide what you're going to do with them. More on reddit.com

Change f(x) to y and it should work More on reddit.com