![]() So it's going to look, it's going to look like Now getting the opposite, the negative of it. Whatever y value we're gonna get before for a given x, you're And so it is now going to look like this. Graph or the whole function by a negative, you're gonna flip it Your whole expression, or in this case, the whole What would that look like? Well if you multiply Let's multiply this times a negative, so y is equal to the ![]() So we have now shifted two to the left to look something, to look something like this, and now, let's build up on that. At x equals negative two, you're gonna kick the cube root of zero, which is right over there. At x equals zero, at x equals zero, or actually, In multiple videos before, so we are now here, and you could even try some values out to verify that. So let's graph y is equal to the cube root of x plus two. Now have an x plus two under the radical sign. So this is already y isĮqual to the cube root of x. I'm just gonna build it up piece by piece. All right, now let's work on this together and I'm gonna do the same technique. Video and try to work it out on your own before we do this together. Y is equal to the cube root of x, and then they say which of the following is the graph of this business? And they give us choices again, so once again, pause this At negative four, we're at three, and at zero, we're at negative one. It to be at negative one, so D is exactly what we had drawn. Look right, but notice, right at zero, we want So let me scroll down here, and both C and D kind of To look something like, something like that. If we were at zero before, we're now going to be at negative one, and so our curve is going If we were at four before, we're now going to be at three. So if we were at six before, we're going to be at five now. We were getting before, we're now just going to Times the square root of negative x minus one look like? Well, whatever y value And then last but not least, what will y, let me do that in a different color. Something like that, so that's y equals two times ![]() Still going to be at zero 'cause two times zero is zero, so it's going to look, it's going to look like that. At x equals negative nine, instead of getting to three, we are now going to get to six. So at x equals negative four, instead of getting to two, we're now going to get to four. Two times the square root of negative x look like? Well, it would look like this red curve, but at any given x value, we're gonna get twice as high. You've essentially flipped it over the y. Square root of negative x is going to look like this. Saw at x equals four, you will now see at xĮquals negative four, and so on and so forth. You saw at x equals two, you would now see at Now this one won't beĭefined for positive numbers. So the square root of x is notĭefined for negative numbers. What would that do to it? Well, whatever was happeningĪt a certain value of x will now happen at the So let's say we want to now figure out what is the graph of y isĮqual to the square root of? Instead of an x under the radical sign, let me put a negative x Y equals the square root of x looks like, but let's say we just want to build up. And the way that I'm going to do that is I'm going to do it step by step, so we already see what Times the square root of negative x minus one should look like, and then I'll just lookĪt which of the choices is closest to what I drew. Through this together, and the way that I'm going to do it is I'm actually going to try to draw what the graph of two Which of the following is the graph of y is equal to two times the square root of negative x minus one? And they give us some choices here, and so I encourage you to pause this video and try to figure it out on your own before we work through this together. \), reflect it through the \(x\)-axis, then shift down \(1\) unit.The graph of y is equal to square root of x is
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