How do you find the domain and range?

Question

I really don't understand this concept....all I know is that it has to be written in interval notation...so for example, here is one problem:

f(x)= x/x^2+2x+4

How would I find the domain and range????!!? If anyone could give me an explanation as to how they are found, and WHY they are found, and a method in finding them it would be greatly appreciated!

Answer 1

The domain is all the possible values of x where the function can be evaluated. The two main things to look for are division and square roots. Division by zero is undefined. So if you can find a value of x that gives a division by zero, that point isn't in the domain. You can't take a square root of a negative number (using only real numbers). So whenever you have a square root, you want to find what values of x make the expression under the square root negative. There are also other things that reduce the domain.

Once you find your domain you have to figure out what output values are possible from the input values (domain) that are possible. This will be your range.