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I need an example for this question:

(g)  a function that has odd symmetry (symmetry with respect to both the x and y axes)

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Related questions

Harmonic function in the ball, PDE

Could someone explain how exactly is P calculated? And why we need apply xy to both b and c?

                                               

                                          

 

Solution. According to hint we look for ʯ in the form (20.3) with P a polynomial of degree 6 - 2 = 4; since g is odd with respect to x and y (separately) so P is; since g is even with respect to z so P is; since g is symmetric with respect to y  x permutation, so P is. Thus and

 

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3. Sketch the graph y = f(x) of a function f, which has all of the following properties. (Note that you are not being asked to give an explicit formula for .) (i) f is an odd function. (ii) / has exactly one root (z-intercept). (iii) The domain of / is the entire real line. (iv) f() has a global (absolute) maximum at x = 2 and this is the only extremum (absolute or relative) of f(c) for all values >0. (v) The graph off is a continuous curve. (vi) The z-axis is a horizontal asymptote off.

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