Believe it or not, one of the main concepts that most students aren’t taught is how to find domain and range of a function. I blame the teacher for this, because it’s very important and also very easy to teach and learn.

It starts with the domain. The basic idea is that you want to exclude any values of x that will make your function undefined or imaginary. In other words, you want to only include values of x that will make your function real.

This is easy to identify. The only time you will have an undefined function is if the denominator is equal to zero. No denominator, no problem.

Similarly, the only time you will have an imaginary function is if the square root is negative. No radical, no problem there. (To be specific, any even root would apply to this case, not just square roots. But I’m trying to focus on the basics right now).

So there you have it: If there is no denominator and no radical, then your domain includes all real values of x. Easy.

As for the range, it describes the upper and lower limits of your function (y) as x is near negative infinity and positive infinity. Both domain and range list the values from least to smallest. Notations may vary, including brackets and inequalities.