The reflection of $f(x,y) = x^2 - y^2$ How would I make a reflection of $$  f(x,y) = x^2 - y^2 $$ along the z axis? Beacuse if if write $$  f(x,y) = -(x^2 - y^2) $$, flips the figure along the XY axis...

Reflection in the $z$-axis takes $(a,b,c)$ to $(-a,-b,c)$.  
