Must help part 2 please

Question

Given y= x^5/x^6+1, use the algebraic tests to determine symmetry with respect to both axes and the origin. 

Multiple Choice, choose correctlt and show work! 

A. Y-axis symmetry only 

B. X-axis symmetry only 

C. Origin symmetry only

D. X-axis, y-axis, and origin symmetry 

E. No symmetry 

Answer 1

Symmetry with respect to the y-axis:  replace x by -x

 

    y = (-x)⁵ / (-x)⁶ + 1

 

    y = - x⁵ / x⁶ + 1

 

   Since the resulting equation is different from the equation given in the statement of the problem, the graph is not symmetric           with respect to the y-axis.

 

   (eliminate choices A and D)

 

Symmetry with respect to the origin: replace x by -x and y by -y.

 

    -y = (-x)⁵ / (-x)⁶ + 1

 

    -y = -x⁵ /x⁶ + 1

 

     The resulting equation is different from the equation given in the problem statement, so we don't have origin symmetry either.  

 

     So, answer C is out.

 

Symmetry with respect to the x-axis:  replace y by -y

 

     clearly, we get an equation that is different from the equation given in the problem statement.

 

     So, there is no x-axis symmetry.

 

ANSWER:  E