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Do you know the vertex equation?
To go from \(x^6\) to \(-3(x+4)^6-8\) you need to do some shifting and turning, use the vertex form to help: \(f(x)=a(x-h)^2+k \) where the vertex is (h, k) and a determines the expansion/shrink.
how would i plug x^6 into the vertex form ? or would i put the second equation into the vertex form? :o
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wait nvm it already is in vertex form
If you look at the graphs, it might be a bit hard to see but as you can see the graph was reflected
http://prntscr.com/7eetq9 and probably has a vertex at (-4, 8)
Any addition or subtraction represents a shift. So in this case you have +4 and a -8. Any multiplication represents some sort of stretch or compression. If the multiplication is by a negative value it will also be a reflection.
The way I kind of explain it is to say is your value "trapped" with x or not? As in can you freely move that number around. So examples of "trapped" are
Where your numbers are being bounded by some sort of grouping symbol.
So, if your transformations are not bound by a grouping symbol, they will affect y-values. So for us, the -3 multiplication and the -8 subtraction are applied to y-values. The +4 is bounded and trapped with x, so it will be the only thing affecting x-values.
Now, transformations that affect y-values do as they look like they might do. If it's a +3 shift, things will go up 3. If it's a multiplication by 2, all the y-values will be multiplied by 2. Now the transformations that affect x-values, the "trapped" ones, kind of do the opposite. If it's a +5, you go left 5, more into the negative values for x. And if you multiply by 2, all the x-values shrink by a factor of 2 (or are multiplied by 1/2 you can say).
So after all that, let's put everything together. Now, we want to consider multiplicative transformations first. The only one of those is the -3. So all the y-values of x^6 were multiplied by -3. In terms of transformations, this represents a reflection about the x-axis and a stretch by a factor of 3. After that, the graph was shifted 4 to the left and down 8.