Question

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Prove that A(-2;-1) is a symetry center for the function y=-1+3/(x+2)?

Answer 1

prove .. well 1/x is a hyperbola so it is symetric by default; moving it around doesnt change that.

a good proof may be to use a circle centered at A and show that for a minimum radius it touches at 2 points

Answer 2

or use transformations:

y = 1/x is centered at 0,0

y = 3/x is centered at 0,0

y = 3/(x+2) is centered at -2,0

y = 3/(x+2) - 1 is centered at -2,-1