Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
akshayb
Group Title
How can one test the symmetry of x axis, y axis and origin?
 one year ago
 one year ago
akshayb Group Title
How can one test the symmetry of x axis, y axis and origin?
 one year ago
 one year ago

This Question is Open

akshayb Group TitleBest ResponseYou've already chosen the best response.0
Please tell the answer.
 one year ago

hewsmike Group TitleBest ResponseYou've already chosen the best response.1
May I assume that you mean test some function for symmetry across the x and y axes and the origin ? :) Generally it means applying some transformation and seeing if there is no change ie. swap x for x and see if f(x) = f(x) so with \[f(x) = x^{2}\]then \[f(x)=(x)^{2} = (1)^{2}x^{2}= x^{2}=f(x)\]if we are plotting this function in two dimensions as \[y =x^{2}\] dw:1359934489024:dwthen this implies symmetry of reflection across the yaxis ( pardon my drawing skills ). Symmetry across the xaxis is likewise. As regards the origin : then that is a reflection across the yaxis and then another reflection across the xaxis. Thus a circle dw:1359935010242:dwis symmetric across x and y axes and hence the origin too. You can deduce this from the equation for a circle, say : \[x^{2}+ y^{2} = 1\]is invariant if we swap x for x and y for y \[(x)^{2} + (y)^{2} = (1)^{2}x^{2} + (1)^2y^{2} = x^{2} + y^{2}\]To be complete I ought mention that reflections across the x then y axes ( or vice versa ) is equivalent to a rotation of 180 degrees around the origin ....
 one year ago

hewsmike Group TitleBest ResponseYou've already chosen the best response.1
Err, the circle was in that second graphic earlier today.
 one year ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.