How do you determine what the domain and range of a function are?

Answer 1

The domain of a function pertains to all the x values

The range of a function pertains to all the y values

So domain and range do not get confused, this can be easily remembered by the order of the how the first letter of the word appears in the English alphabet.

d, domain, goes before r, range

x goes before y

domain = x values

range = y values

ill try to add to the previous writer.

previously, he wrote what the domain and range are for easier functions, but not how to determine them.

more generally, what the domain is, is what you can put into a function, which in simpler cases, is jus x. to find what you can put in, it helps to find what you cant put in for x, meaning, where is the graph of the function discontinuous. for example, if we look at the function f(x)=1/(1-x) if we put 1 in for x, then the denominator goes to zero and the function is discontinuous at that x value, therefore 1 will not be included in the domain, but everything else will be included since there are no other disconinuities. the domain will end up looking like this-

(-infinity,1), (1,infinity). now for the range, all you have to do is find what you can get out of the function from what you can put in, which can usually be done by putting the values you see for the domain in. putting negative infinity in for x in

f(x)=1/(1-x) you get zero and putting one in you get infinty. putting it together you get (-infinity,0), (0,infinity) for your range.

p.s. as i stated before, more generally, your domain is more so what you put into your function, so it is not always x, for example, in the case of a function of 2 variables such as f(x,y), what you can put in for both x and y will make up your domain, not just x, and y will most certainly not be your range, rather it will be the values of f(x,y).