![]() ![]() Is to shift to the left or the right, we can replace our x with an x minus something, so let's see how that might work. The left or to the right? So what's interesting here That amount to x squared so it changes, we could say the y value, it shifts it up or down. And that's pretty intuitive, 'cause we're adding or subtracting To set what k is equal to, so here, k is equal to one, so this is x squared plus one, and notice, we have shifted up, and if we increase the value of k, notice how it shifts the graph up, and as we decrease the value of k, if k is zero, we're back where our vertex is right at the origin, and as we decrease the value of k, it shifts our graph down. Then we can add a slider k here, and this is just allowing us With the variable k, then let me delete this little thing here, that little subscript thing that happened. ![]() And we can set up a slider here to make that a little bit clearer, so if I just replace this with, if I just replace this Now it is at zero, negative three, so it shifted it down. If we subtract one, or actually, let's subtract three. Whatever f of x was before, we're now adding one to it so it shifts the graph up by Value of f of x higher so we can add a value, and that does look like Well one thought is, well, to shift it up, we just have to make the That looks as we would expect it to look, but now let's think about how How do things shift to the right or left or how do they shift up and down? And what we're going to start off doing is just graph a plain vanilla function, f of x is equal to x squared. So I am here at, which is an online graphing calculator, and the goal of this video is to explore how shifts in functions happen. ![]()
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