Graphing Radical Equations using a Table - Problem 3

I’m going to be graphing this radical function using a table of values a lot of you guys are going to be learning shifting rules if you haven’t already. So some of you guys will be able to graph this without making the table. But I want to show you how a table will always work.

Before I make the table the problem asked me to find the domain and we know that the square root of a negative number is a non-real solution. So whatever is under the square root in my problem, in this case it’s 2x, has to be non-negative. I’m going to write that as greater than or equal to 0. If I solve for x for both sides by dividing by 2, I’m just going to get that my x numbers need to be greater than or equal to 0, that’s my domain. That’s half the problem done.

So now when I’m making my table of values I’m going to choose x numbers that are bigger than or equal to 0 and then plug them in one at a time. So let’s do it. Be really careful with the order of operations you need to multiply your x number by 2 then square root it and then add 1.

So here we go, 2 times 0 is 0, square root it, it’s still 0 plus 1. 2 times 1 is 2, square rooted is 1.4 plus 1 I’ll have 2.4, 2 times 2 is 4 square root of 4 is 2 plus 1 is 3. 3 times 2 is 6, 6 square rooted is something that I didn’t write down but I know that when I add 1 to it I get 3.45, yeah I do, 3.45. I’m going to grab my calculator so I don’t leave you hanging here.

2 times 4 is 8 the square root of 8, let me grab my calculator. Square root of 8 is 2.83 and then I need to add 1 to it so I’ll have 3.83. Those are the points that I’m going to put on my graph. Again that was really important that I follow the order of operations, multiply by 2 first and then square root and then do the adding 1.

Okay let’s get this guy on the graph and you're going to see we are going to have what we call a dilation. It’s not going to be the usual width of our radical function graph it's going to be a little bit different. Let me show you.

Okay so our first stop was at (0,0) our next stop was at (1,2.4), sorry I’m totally blocking this you guys got to trust me (1,2.4) then we have (2,3), 3 and a halfish and then 4 close to 4, 1 2 3 4 close to 4 okay. So I have my usual curvy shape only this guy‘s a little bit wider here and the reason why it’s a little bit wider is because I’m multiplying inside the square root, I’m multiplying by 2.

So sometimes you get parabola shapes on their sides that are wider or skinnier depending on if you have a dilation, in our case we have that 2x inside the radicand.

Again the last thing I’m going to tell you is to make sure that you have a dead end at one side and an arrow on the other because my domain tells me my x numbers cannot be smaller than 0, they have to be numbers that are greater than or equal to 0.