Symmetry of a graph. SymmT(A)?

[Matriculator]

I've tried looking all over, but haven't been able to find explanations. I was wondering if anyone could provide me links to learn more about these- what's in the picture. Or if you can explain. I have already turned this work in so I'm not looking for the answers, I want explanations. I know how to reflect the figures but what do they mean by SymmT(A) sets? Thank you.

 

[Simon Bridge]

Can you sketch the graphs that result from the transformations?
$Symm_T(A)$ is something special to your course?

 

[Matriculator]

Can you sketch the graphs that result from the transformations?
$Symm_T(A)$ is something special to your course?

Yeah. The first one will result in an upside down(in relation to the first) parabola, with the same Xs but different Ys, it will be located in the 4th quadrant.

The second one just flips over the Y-axis retaining the Ys but having different Xs. It'll be located in the 2nd quadrant.

I know how to all all of this, but my question is whether that's all I need to do in this case. Or do I need to find the $Symm_T(A)$, based on the question asked. I'm not sure of what's that exactly. I'm trying to learn more about it but whenever I look online, nothing of the sort comes up. This is for a pre-calc class.

 

[haruspex]

As Simon indicated, you need to know the definition of SymmT, and it does not appear to be anything standard. It must be defined in your course notes somewhere.

 

[Matriculator]

As Simon indicated, you need to know the definition of SymmT, and it does not appear to be anything standard. It must be defined in your course notes somewhere.

Oh, sorry about that. It's from this lesson. Thank you all very much for helping. This is driving me nuts. I've been a lot behind on my college courses, but I need to know this. Except for this sheet in class and explanations which I wasn't following through well due to a lack of sleep the previous night, there's literally nothing else including the textbook, which these don't seem to be a derived from, that I can learn about this.

 

[skiller]

Oh, sorry about that. It's from this lesson. Thank you all very much for helping. This is driving me nuts. I've been a lot behind on my college courses, but I need to know this. Except for this sheet in class and explanations which I wasn't following through well due to a lack of sleep the previous night, there's literally nothing else including the textbook, which these don't seem to be a derived from, that I can learn about this.

And there you have your definition of Symm_T immediately prior to Example 10 in your pdf.

You keep applying the transformation to the initial set and take the union of your results. In the case of a simple reflection, then you only need to apply the transformation once to obtain the final set. (Can you see why?) But if the transformation is, for example, a rotation of a quarter-turn clockwise around the origin, then you need to apply it 3 times. (Again, can you see why?)

 

[haruspex]

Ok, so $Symm_T\left(A\right) =\bigcup_{k=0}^\infty T^k\left(A\right)$. Can you make progress now?