Question

Which of the following is the graphed below

Answer 1

Answer:

$A.\:y=\left \{ {{x^3-3,x\le2} \atop {x^2+6,\:x>2}} \right.$

Step-by-step explanation:

The quadratic function has equation $y=x^2+6$ and the cubic function has equation $x^3-3$.

The function $y=x^2+6$ is defined on the interval $x\:>\:2$.

The function $y=x^3-3$ is defined on the interval $x\:\le 2$

The required piece-wise function is

$y=\left \{ {{x^3-3,x\le2} \atop {x^2+6,\:x>2}} \right.$