MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
Solving rational equations is substantially easier with like denominators. When solving rational equations, first multiply every term in the equation by the common denominator so the equation is "cleared" of fractions. Next, use an appropriate technique for solving for the variable.
Whenever you're asked to graph anything in Math class, the most basic way to create a graph is using an xy table. That's what we're going to look at today in graphing rational functions. Excuse me radical functions, we're not doing rationals. Radicals. It's a big difference.
Okay, so first thing you want I want to remind you guys is of domain and range. The domain is the set of all possible input values. That's really important when it comes to square roots because you guys know the square root of a negative number is not a real value, is not a real solution. So in order to find the domain, the radicand must be greater than or equal to zero. Let me show you what I'm talking about. If I want to take the square root of something, this thing whatever it is, I'm drawing a little cloud. That cloud or the radicand has to be greater than or equal to zero. That's how you find the domain of a radical function.
Like in this problem for example, we're going to look at the parent function. In order to find the domain or my x values that I'm going to put in my table, I'm going to start by setting my radicand greater than or equal to zero. Radicand is whatever's under the square root. All I have was x so all I need is x is greater than or equal to zero. That tells me when I'm setting up my table that I want to use x numbers that are zero or bigger. I don't want to use any negative values because that would be non-real solutions in this function.
So let's go through and plug in these x numbers one at a time and find their corresponding y numbers. If I stick in the square root of zero, if I just put in zero there, square root of zero is zero. Square root of one is one, square root of two, I'm going to approximate the decimal with 1.41, you can check that on your calculator. Square root of three when I stick that in there, I get 1.7 something, 1.73 I think, and then I'm going to stick in 4. Square root of 4 you guys know, is 2.
Okay. So now I have a good number of points. I'm going to get these guys on the graph and you'll see the shape that all radical functions have. Here we go. I first start with 0 0, then I had 1 1, 2 1.4, that's like almost one and a half. I have to approximate a little bit. 3 is 1.7 and then 4 was 2.
Okay. So you can kind of see what this is looking like. It's not a straight line. What this is, is like half of a parabola on it's side. This curve continues forever and ever. It goes out in this direction out forever and ever, but notice how it stops right there at the end. That's because my domain was only x numbers that were bigger than or equal to zero. My graph doesn't continue in that directions. Please don't put an arrow on that side because it doesn't continue. It just stops right there at zero and then it heads out in this direction.
So all of the graphs that you're going to be doing by making a table or any time you graph a radical function, it's going to have this half parabola shape. It's going to be having like a dead end on one on one side and then an arrow on the other side that continues out forever and ever.
When you're making your table, be sure to be clever about what x values you choose. Use the domain to tell you what x numbers are possible. That is take the radicand, set it greater than or equal to zero and then solve for x in order to find what x number should go to your table.
