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We're asked to graph the function f(x)

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is equal to the principle square route of .5x-1

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And to graph it we're going to just sample some points

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some x values that are within the domain of this function,

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this function definition, and see what the function is equal to

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for those x values, and then we can connect those dots

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and see what the curve will look like

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So, let me do a little table here, and so I'm going

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to pick some x-values, and I'm going to figure out what

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the f(x) values are given those x values

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And actually, I'm going to do something in between

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because I want to have nice, clean numbers

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I want to pick x-values that are nice clean integers

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and I want to get f(x) values that are nice clean integers

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So I'm going to be a little bit more careful

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in what x values I pick.

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I wanna pick x values so that this part of the expression

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this part of the function definition

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ends up being an integer

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and if this needs to be an integer, then what's underneath

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the radical, that .5x

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that needs to be a perfect square

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So, let me make another column over here

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just to make our math a little bit cleaner

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You could pick just arbitrary x-points

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you could pick x to be 1, 2, 3, just go like that

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but on some of those you might get strange radicals

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over here, which might be hard to graph without a calculator

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So let's try so let me write over here what 0.5x is

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And I'm doing this just so that I can pick this

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we want this thing over here

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to be perfect squares

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because if 0.5x is a perfect square, than the square root

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of that is going to be an integer

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So let's say that 0.5, let's think about all

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of the perfect squares, you can start at 0, then you

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could go to 1, then we could go to: 2 isn't a perfect

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square, 3 isn't a perfect square,

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I'm just thinking of all the values where if I took the

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square root, I'd get an integer

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And then I go to 4, then I go to 9, then I go to 16

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and then I go to 25.

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These are the first five perfect squares, obviously

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with 0, if you take the principle square root of that you get

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zero. So these would be good values for

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.5x. But if those are what .5x is equal to, what is

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x going to be? So, if 0.5x is 0, then x

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is also going to be 0. You could solve that

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separately over in an equation right over here

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you could say 0.5x is equal to 0,

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x is equal to 0 divided by .5, just divide both sides

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by .5, and you get that equal to 0.

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So in general, to get what the x-value is, we

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jsut have to take this number and divide it by .5

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or another way of thinking of that is just taking

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this number and multiplying it by two.