It *might* be eaiser for me to find transformations from complex to simple fuctions not how you did them, but by finding the transformations the opposite way. The only problem is how to do the opposite of a dilation, reflection and translation?
It is possible to find the transformations by doing the problem in reverse, but it isn't easier. In terms of what the opposites are, you need only think about this logically. The opposite to translating to the left by 3 is to translate to the right by 3, the opposite of reflecting something in the x-axis, is to again reflect it back in the x-axis, the opposite of dilating by a factor of 3 from the y-axis, is to dilate by a factor of 1/3 from the y-axis. But, you also need to be careful to reverse the order! It's honestly not simpler to do it this way.
I assume you're referring to the transformations affecting the y-coordinate here? (Note that the translation affecting the x-coordinate has incorrectly been stated as "up", when it should be "right"). There are two tranformations affecting the y-coordinate: dilation by factor 1/2 from the x-axis and reflection in the x-axis. The former means multiplying the y-coord by 1/2 and the latter means multiplying the y-coord by -1. Regardless of the order you do this in, you still end up with -1/2*y. So in *this* instance, you can reverse the order, listing the dilation before the reflection. But as a general rule, DRT is an incredibly dangerous way to teach transformations. Any sequence of transformations can often be listed in multiple correct ways and it's important that you understand your transformations well enough to see that. For example, if I have (x, y) -> (x, -2y+4), then this could be described as a dilation by a factor of 2 from the x-axis, followed by reflection in the x-axis, followed by translation up 4 (which is DRT), but it's also correct to swap the dilation and reflection in this instance. It's also correct to write this same transformation as (x,y) -> (x, -2(y-2)), in which case you translate down by 2, then dilation by factor 2 from the x-axis and reflection in the x-axis (these latter two transformations can be given in either order). Or alternatively the same tranformations could be written as (x,y) > (x, 2(-y+2)), in which case you reflect in x-axis, then translate up 2 units, then dilate by factor 2 from x-axis. All are correct sequences of transformations. You must understand transformations well enough to see that these are all the same. DRT is unnecessarily misleading. There's no reason to give a sequence of transformations in the order DRT, and sometimes your answer will be incorrect if you think transformations must always be given in the order DRT.
Thanks a lot, excellent effort
Thank you. I'm glad you found it helpful!
Thank you soooo much! you have a special place in heaven !
Something to look forward to!
It *might* be eaiser for me to find transformations from complex to simple fuctions not how you did them, but by finding the transformations the opposite way. The only problem is how to do the opposite of a dilation, reflection and translation?
It is possible to find the transformations by doing the problem in reverse, but it isn't easier. In terms of what the opposites are, you need only think about this logically. The opposite to translating to the left by 3 is to translate to the right by 3, the opposite of reflecting something in the x-axis, is to again reflect it back in the x-axis, the opposite of dilating by a factor of 3 from the y-axis, is to dilate by a factor of 1/3 from the y-axis. But, you also need to be careful to reverse the order! It's honestly not simpler to do it this way.
17:47 Is it really incorrect if you said dilation first, because what about DRT?
I assume you're referring to the transformations affecting the y-coordinate here? (Note that the translation affecting the x-coordinate has incorrectly been stated as "up", when it should be "right"). There are two tranformations affecting the y-coordinate: dilation by factor 1/2 from the x-axis and reflection in the x-axis. The former means multiplying the y-coord by 1/2 and the latter means multiplying the y-coord by -1. Regardless of the order you do this in, you still end up with -1/2*y. So in *this* instance, you can reverse the order, listing the dilation before the reflection. But as a general rule, DRT is an incredibly dangerous way to teach transformations. Any sequence of transformations can often be listed in multiple correct ways and it's important that you understand your transformations well enough to see that. For example, if I have (x, y) -> (x, -2y+4), then this could be described as a dilation by a factor of 2 from the x-axis, followed by reflection in the x-axis, followed by translation up 4 (which is DRT), but it's also correct to swap the dilation and reflection in this instance. It's also correct to write this same transformation as (x,y) -> (x, -2(y-2)), in which case you translate down by 2, then dilation by factor 2 from the x-axis and reflection in the x-axis (these latter two transformations can be given in either order). Or alternatively the same tranformations could be written as (x,y) > (x, 2(-y+2)), in which case you reflect in x-axis, then translate up 2 units, then dilate by factor 2 from x-axis. All are correct sequences of transformations. You must understand transformations well enough to see that these are all the same. DRT is unnecessarily misleading. There's no reason to give a sequence of transformations in the order DRT, and sometimes your answer will be incorrect if you think transformations must always be given in the order DRT.
Great video thanks
why is that up i thought its right 17:43
Yea she made a mistake