Answer:
[tex]A.\:y=\left \{ {{x^3-3,x\le2} \atop {x^2+6,\:x>2}} \right.[/tex]
Step-by-step explanation:
The quadratic function has equation [tex]y=x^2+6[/tex] and the cubic function has equation [tex]x^3-3[/tex].
The function [tex]y=x^2+6[/tex] is defined on the interval [tex]x\:>\:2[/tex].
The function [tex]y=x^3-3[/tex] is defined on the interval [tex]x\:\le 2[/tex]
The required piece-wise function is
[tex]y=\left \{ {{x^3-3,x\le2} \atop {x^2+6,\:x>2}} \right.[/tex]
