explain how to test algebraically for all three types of symmetry.
Test y= 2^x2/x^2+1 for all three types
What symmetry is found for this graph?

Question

explain how to test algebraically for all three types of symmetry.
Test y= 2^x2/x^2+1 for all three types
What symmetry is found for this graph?

anonymous · Answer

it is even so it is symmetric wrt the y axis for sure

anonymous · Answer

This expression is y as a function of x, so it can't be symmetric wrt the x axis.

Even functions allow us to substitute -x for x and get the same output.  Since all the x terms are squared, this is true here.  Even functions are symmetric wrt the y axis.

If a function is even, the only way it can be odd also is if it is uniformly zero.  Not the case here, so it does not have symmetry wrt the origin.

anonymous · Answer

How do I test the problem y=2^x2/x^2+1?

anonymous · Answer

Test for symmetry wrt x axis:  Substitute -y for y, and see if the resulting expression is true.

Test for symmetry wrt y axis:  Substitute -x for x, and see if the resulting expression is true.

Test for symmetry wrt origin:  Substitute both -x for x, -y for y, and see if the resulting expression is true.