How to Find the Range Without Graphing

Hi, I'm Rachel, and today we're going to be going over how to find the range without graphing. Well, we're going to have to look at the problem algebraically, and we're going to have to look at the y, because the domain deals with the x values and the range deals with the y values. So, let's say that we have an equation like y equals one over x-squared plus four. Well, we know here for the range that it's going to always be positive, right? Because the square root of a number here for x, it's always going to be a positive value. So, the lowest it can be is zero. Now, if we plug in zero for x, that's the lowest possible thing, we get zero plus four, right? I'll show here, one equals zero-squared plus four, that's one over four. So that is one-fourth, zero one-fourth is the range. And that's how we write it. We know that it can't be a negative number, right? Because that's just impossible with this solution, and there we found the range and we didn't even have to graph it at all. I'm Rachel and thank you for learning with me today.