Let's say, we tried thisįor e to the x power. And so that's why itįlips it over the y-axis. It now takes that value on the corresponding opposite value of x, and on the negative value of that x. So, whatever value theįunction would've taken on at a given value of x, But when x is equal to negative one, our original function wasn't defined there when x is equal to negative one, but if you take the negative of that, well now you're taking Principle root function is not defined for negative one. Now what about replacingĪn x with a negative x? Well, one way to think about it, now is, whenever you inputted one before, that would now be a negative one that you're trying toĮvaluate the principle root of and we know that the Is going to flip it over, flip its graph over the x-axis. So hopefully, that makes sense why putting a negative out front of an entire expression Of getting positive three, you now get negative three. Of getting positive two, you're now going to get negative two. When x is one, instead of one now, you're taking the negative of it so you're gonna get negative one. Gotten of the function before, you're now going to That's in the expression that defines a function, whatever value you would've Negative out in front, when you negate everything Now, why does this happen? Well, let's just start with the g of x. The x-axis and the y-axis to go over here. Outside the radical sign, and then, I'm gonna take the square root, and I'm gonna put a negative Know, k of x is equal to, so I'm gonna put the negative Well, we could do a, well, I'm running out of letters, maybe I will do a, I don't And then, pause this video, and think about how you If we replace it, that shifted it over the y-axis. Going to happen there? Well, let's try it out. Instead of putting the negative out in front of the radical sign, what if we put it under the radical sign? What if we replaced x with a negative x? What do you think is
Now instead of doing that way, what if we had another function, h of x, and I'll start off by making When I put the negative, it looks like it flipped To happen when I do that? Well, let's just try it out.
Put a negative out front right over there? What do you think is going But what would happen if instead of it just being the square root of x, what would happen if we So no surprise there, g of x was graphed right on top of f of x. Now, let's make another function, g of x, and I'll start off by also making that the square root of x. Had a function, f of x, and it is equal to the square root of x. Use this after this video, or even while I'm doing this video, but the goal here is to thinkĪbout reflection of functions. You can use it at, and I encourage you to Here, this is a screenshot of the Desmos online graphing calculator.
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