Graph the equation y = x + 1 y=\sqrt{x}+1 by choosing points that satisfy the equation. ( Hint: Choose positive numbers only )

Hey, everyone. Welcome back. Hopefully, you get a chance to try this practice problem on your own. But in this problem, we're gonna graph the equation y equals the square root of x plus 1, and we're gonna do this by choosing points that satisfy the equation. Notice how we're not given any x x values to plug into our equation, so we're gonna have to go pick some ourselves. And the problem tells us we're not we wanna choose positive numbers only. So So let's get started. Remember, the first step of solving these kinds of problems is you wanna isolate y to the left side. You want y equals and then everything else on the right. We actually don't have to do anything with this problem with this equation because it already is isolated for y on the left side. So really just gonna put here that y equals square root of x plus 1. Don't have to do anything. Alright? So the next thing I wanna do is I wanna calculate y values for 3 to 5 chosen x values. Alright? So I wanna choose a bunch of x values and plug them into my equation, get y values, and get the coordinate pairs. Now the problem tells us to choose positive numbers only because you actually can't stick negative numbers inside of square roots. Remember, if you try to do something like square root of negative one, you can't do that. It'll give you an error. Right? In fact, if you plug it into your calculator, it won't give you an answer. Answer. Alright? So we're gonna have to choose positive numbers only, and what I'm gonna do is I'm gonna choose the numbers 0, 1, 2, 3, and 4. Plugging in 0 in a square root is perfectly fine, so that's perfectly fine to sort of evaluate into your expression. Alright? So let's go ahead and get started with calculating the y values. Remember, all we're doing is we're literally just replacing the square root of x with the square root of whatever number we're plug we're plugging in. Alright? So here we're just gonna do square root of 0+1, and square root of 0 actually just turns out to be 0. So this really just turns out to be 1 for my y coordinate. Alright? So that means that the coordinate 0 comma 1 is one of my ordered pairs, but we'll figure all those out later. Right? So here what I'm gonna do is gonna do square root of, or sorry, y equals the square root of 1+1, and the square root of 1 is just 1. So this ends up just being 1+1, and this is 2. So the ordered pair is just equal to 1, comma, 2, and we can keep going. Alright? So if I plug in 2 into this expression, right, you're gonna get square root of 2. You just replace this x with whatever number and then plus 1. So the square root of 2, if you try to work it out, it's not just one of those things that you sort of memorize. It's something you you you could just plug into your calculator. And if you try to plug in square root of 2, what you're gonna get is you're gonna get 1.41. So this is really kind of like an approximation or estimation. I'm gonna round this to 1.41 plus 1. And if you work this out, this is gonna be 2.41. So that means that the coordinate here is 2.2.2 comma 2.41. Now let's do the same thing with the square root of 3. If If you try to plug in the square root of 3 into your you know, if you try to figure that out, it's not a nice number, so you're gonna have to plug it into your calculator. And what you'll see when you get this is it's about 1 point 73. So it's approximately 1.73, then we add the 1, and therefore, this whole value is equal to 2.73. So our coordinate is 3 comma 2.73. Last but not least, we've got y equals square root of 4, and the square root of 4 plus 1, the square root of 4 is just 2, so this is just 2 plus 1. And, therefore, our coordinate our y value is 3. So, therefore, this coordinate over here is 4 comma 3, and now we have our 5 ordered pairs. So now we're done with steps 23 or sorry. We're done with steps 2. Now we move on to step 3. We're gonna plot all of these ordered pairs on our graph over here, and then we're gonna connect them with a line for our final step. So here, our first ordered pair is the is the point 0 comma 1, and that's gonna be right over here. Our next point is gonna be 1 comma 2, so that'll be right over here. And And then what we got is we got 2 comma 2.41. So what happens here is we don't necessarily have a nice sort of number. This is like a decimal. And, really, what's gonna happen is we're gonna go to 2 and the x, and then we're gonna go to about halfway between 23. It's not 2 and it's not 3. It's about 2.4, which is almost about halfway. So you can basically sort of plot this point right about here. That's probably like a good guessing point. Alright? So for some of these, you're just gonna have to kind of guess where the points are, based on their values. Alright. So let's go to the next one, which is 3 comma 2.73. So this is a little bit higher, but it's still not quite 3 yet. So you're gonna go 3 in the x, and and you're gonna go up to 3, but that's too far. So we're gonna have to go a little bit sort of down from 3, about 3 quarters of the way up. And it's about the it's gonna be about there when you plot that points. The last point is actually like a nice sort of point. It's gonna be 4 comma 3. So this is gonna be over here. Alright? So now we're done with step 3, and now we just have to connect the lines with the slow the line sorry. Connect the points with a line or a smooth curve. In this case, you can't sort of draw a line that goes through all of the points, because it sort of curves. And if you see if you try to sort of draw a line, it don't it won't pass through all the points. So, really, this is gonna be a smooth curve, and you're basically just sort of connect gonna connect them as smoothly as possible, and it's gonna look something like this. Alright? So this is the graph of the the square root function kind of looks like, and that's all there is to it. So this is and this is gonna keep going on like this over here. Notice how I can sort of draw a little arrow like this because, remember, I can't plug in negative numbers for this. So it really kinda starts here and then just goes off in this direction. Alright? So that's how to graph something like the square root of x. Thanks for watching. Let me know if you have any questions.

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Graph the equation y=x+1y=\(\sqrt{x}\)+1 by choosing points that satisfy the equation. (Hint: Choose positive numbers only)

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Graph the equation $y = \sqrt{x} + 1$ by choosing points that satisfy the equation. (Hint: Choose positive numbers only)