When I want to find the domain of a radical function the most important thing to keep in mind is that the radicand cannot be negative. The stuff under the square root has to be greater than or equal to 0. That’s how to find the domain.
Look at this stuff under the square root it’s the quantity x plus 1. I don’t care about that minus 2 business because that’s not under the square root, my domain comes from this inequality. I got to find x values that are going to be greater than or equal to -1. That’s my domain. Any x value I substitute in to my function that’s greater than or equal to negative 1, would give me a real solution. If I chose like -2, I would get a non real solution I’d have the square root of a negative number and that doesn’t make much sense.
Okay so what I’m going to do is make my x/y chart using x numbers that are bigger than or equal to -1. You have to be really careful when you substitute them in that you follow the order of operations. You're going to add one first, square root that result then subtract 2. So let’s do a couple together.
If I take -1 for my x number -1 plus 1 is 0, square root of 0 is 0 and then take way 2. Careful with order of operations, 0 plus 1 is 1, square root is 1 is 1 take away 2. 1 plus 1 is 2 square root of 2 is 1.4 and then I have to do 1.4 take away 2 and you get -.58 I think. You can double check that on your calculator, be really careful with the order of operations. If I do 2 plus 1 there that’s 3, square root of 3 is 1.7 then I have to do 1.7 take away 2 and I get -.26.
Last but not least 3 plus 1 is 4, the square root of 4 is 2, 2 take away 2 is 0. Okay so I have my bunch of good points that I chose using my domain I’m going to get these guys on the graph. My first point is going to be (-1,-2), then I have (0,-1), (1,-.58) I’m just going to approximate like around to halfish and then (2,-.26) and then (3,0). Those are the points from my graph.
You can see how the shape is starting to come together, be really careful that I don’t put an arrow on that side, it’s a dead end that ends with that closed circle at (-1,-2). It does however have an arrow on this side because my domain continues to all x values that are greater than or equal to -1.
Once you have that set up you guys are ready to go, you have your graph, you’re a happy camper just make sure when you are doing these tables you are really careful with the order of operations. Substitute your x value into the radicand which is under the square root, take the square root before you do any additional adding or subtracting.
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