Answer:
B. [tex]y= \left \{ {{x^{2}+4,\,x< 2 } \atop {-x+4,\,x \ge 2}} \right.[/tex]
Step-by-step explanation:
The piecewise function consists in two functions:
(i) A vertical parabola directed in the +x direction and centered at [tex]V(x,y) = (0, 4)[/tex] for all [tex]x \in (-\infty, 2)[/tex]. That is:
[tex]y = x^{2}+4[/tex], [tex]x < 2[/tex]
(ii) A line with negative slope for all [tex]x \in [2, +\infty)[/tex].
[tex]y = -x+4[/tex], [tex]x \ge 2[/tex]
The correct answer is B.
