Symmetry with Functions!
The last couple of classes in math we have been learning about symmetry with relations and functions. We learned that if something is symmetric over the X-Axis, the (x.y) coordinate implies that there will be a (x,-y) coordinate as well. In the case of something being symmetric over the Y axis there will be an (x,y) coordinate along with a (-x, y) point. If something is symmetric over the origin there will be an (x,y) point and a (-x,-y) coordinate.
An even function = symmetry over Y axis (to test for even plug in -x)
An odd function = symmetry over origin (to test for odd plug in -y)
A problem that might present it's self with symmetry will look something like this...
5y=2x^2-3
There are two ways to solve this, one being algebraically the other is using a calculator.
We also learned about transformations with functions
These transformations include....
Vertical shift
horizontal shift
reflection over the x or y axis
vertical stretch or shrink
horizontal stretch or shrink
Say you have an set like f(x)=sinX Versus 2f(x)=2(sinX)
Plug these forms into your graphing calculator and graph the functions.
This one turns out to a vertical stretch because of the 2's in the second equation.
This link has quality examples of what an Y-axis, X-axis and origin symmetry looks like
http://library.thinkquest.org/20991/alg2/quad2.html
This is a great first blog post for our blog, and I really do appreciate the ThinkQuest link. I think including some examples and explanations of other transformations would improve this post, however.
ReplyDeleteI agree with Wasita that this is a great first presentation, but when you give the symmetry problem, you could have listed the factors that transform the function. For instance 5y shows that there will be a vertical stretch. 2x shows a horizontal shrink. and the -3 shows that there will be a vertical shift down. Overall you made a high quality post.
ReplyDeleteI think this post is a good example for what later bloggers should follow. It helped me understand the previous lesson in some areas where I was confused. One place I would improve is when you say that you can solve equations algebraically or with a calculator, I would give an example of solving one with algebraically. Overall, I thought this was a very good post.
ReplyDeleteThis is a really good start! Some basic ideas and some more detailed instruction for some of the topics. It would be super helpful to have instructions on how to complete the transformations, and maybe one or two examples to help identify each one, but besides that this is looking good!
ReplyDeleteJack, I appreciate your willingness to be A Blocks first blogger. Your post contains a broad overview of symmetry and transformations. However, more specificity and depth would have enhanced it. For instance, your first paragraph uses the word "something" instead of "function." Also, your test for odd symmetry is not accurate - to test if a function is odd you need to plug -x in for x and -y in for y. If this substitution results in the same function as your original, then it is odd.
ReplyDeleteYour symmetry example was a little confusing. You did not pose a question or an answer. I'm guessing the question was something like "Does the equation below contain any symmetry? Is it symmetric over the x-axis, y-axis, origin, or none of the above?" A solution outlining the process for answering this question would have been ideal.
Your list of transformations accurately covers the different types we explored in class. On that day, you were introduced to these transformations via examples that you graphed and analyzed. A description of this process and any questions you might have had would have been a good way to wrap up your post.
Finally, your link was an excellent resource and it contained some nice examples.
In future posts I would encourage you to dig a bit deeper. Also, reference the blog post rubric, as you did not include anything from category #2.