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Question 668508: How do u know the differences between domain and range . How do u find the range.
Answer by swincher4391(1107)   (Show Source):
You can put this solution on YOUR website! Domain and Range are inversely different in fact. The way that I learned about domain and range is like this:
Say you have a machine. That's your function f. Now say the machine takes a certain input x, that's your domain. Whatever comes out of the machine is f(x), which is your range.
So to answer your question more adequately: in a function f, the input x is your domain while the output f(x) is your range. In order to find the range, you must consider all domains that are defined for your function. For example let's say f(x) = x^2.
What is the domain of x^2? Well, there is nothing that we can put in that will make our function undefined. So from  ,  is our domain. However, what is our range? First, will we ever get a negative number for f(x) = x^2? If we put in a negative domain we get a positive answer and if we put in 0 we get 0 and if we put in a positive we get a positive answer, so our domain is from 0 to .
Let's try one more. Consider f(x) = 1/x. What is our domain? The only "bad spot" is when x = 0. We are dividing by 0 and thus f(x) is undefined. Now, what is our range? What if x is negative? We should get all negative values. Can f(x) ever be 0? The only way we can be 0 is if the numerator is 0, so 0 is not in our range. Similar to negative values, if we are to put positive values, we'll get all positive answers and so we get that our range is from , except 0.
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