To the left by three, and I encourage to think about why that actually makes sense. If you replaced x with x plus three, it would have had the opposite effect. Indeed shifted to the right by three when we replace The same behavior that you used to get at x is equal to one. And you can validate that at other points. Well, the way that we can do that is if we are squaring zero, and the way that we're gonna square zero is if we subtract three from x. When x equals zero for the original f, zero squared was zero. Think about the behavior that we want, right over here, at x equals three. So this is what the shiftedĬurve is gonna look like. Once again, I go into much moreĭepth in other videos here. Why does this make sense? Well, let's graph the shifted version, just to get a littleīit more intuition here. Is increasing by three, but I'm replacing x with x minus three. Of it being x squared, you would replace x with x minus three. Would be y is equal to f of x minus three, or y is equal to, instead To the right by three, you would replace x with x minus three. But in general, when you shift to the right by some value, in this case, we're shifting
Now, some of you mightĪlready be familiar with this, and I go into the intuition in a lot more depth in other videos. Would we change our equation so it shifts f to the right by three, and then we're gonna shift down by four. We're gonna first shift to the right by three. Make the vertices overlap, but it would make theĮntire curve overlap. In the vertical direction, that not only would it
Least visually, in a little bit, so I'm gonna go minus four And it does look, and we'll validate this, at I would be able to shift the vertex to where the vertex of g is. And if I focus on the vertex of f, it looks like if I shift that to the right by three, and then if I were to shift that down by four, at least our vertices would overlap. And on a parabola, the vertex is going to be our most distinctive point. Shifting a parabola, I like to look for a distinctive point. All right, so whenever I thinkĪbout shifting a function, and in this case, we're Now, pause this video, and see if you can work Be thought of as a translated or shifted version of f of
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